Go back to your electric fence and do it right. Doesn't have to be expensive if you do it yourself. My neighbor has goats that used to be mine because I got tired of working on the fence. Our situation made electric fences a PITA so they did just what you said. As soon as they got on his side, they wanted back on my side.
Anyway, don't be stingey with the wire, and make sure your charger is grounded very good. Then, run your fence with bare wire (not rope or tape) and start it close to the ground, alternate hot and ground. Just googled this, may be helpful for you.

High-tensile, smooth wire, electric. Probably, the most effective and economical goat fence is a smooth wire, high-tensile electric fence, so called "smooth wire" because the wires aren't barbed and "high-tensile" because it is constructed of high tensile wire that can be strung extremely taut without breaking. Due to the greater tensile strength of the strands, high-tensile wire can be pulled tighter than standard electrified wire, which tends to sag over time.

High tensile, electric fences require strong corners and end braces. Five, six or seven 12 gauge high-tensile wires are recommended for goats. The bottom wires of the fence should be more closely spaced than the top. Wire spacings of approximately 6, 5, 5, 8 and 10 inches are common. In areas where there is relatively even rainfall and some green vegetation most of the year, it is recommended that all wires be hot. Ground return wires are recommended where there is low rainfall, stony and dry soil conditions or where the ground is frequently frozen or snow covered. It's a good idea to install switches so that wires can be grounded when the grass is tall or other situations warrant.

The charger (or energizer) is the "heart" of the electric fence system. It converts main or battery power into a high voltage pulse or "shock" as felt by the animal when it touches the fence. In the past, electric fence chargers shorted out easily. Today's chargers are low impedance, meaning they are designed to effectively shock though vegetation and other foreign materials touching the fence. A 4,000 volt charger is sufficient for goats. The number of joules needed depends on the length of the fence, the number of electrified wires and the severity of conditions. A joule is the amount of energy released per pulse. As a general rule, 1 joule will power 6 miles of single fence wire; 4.5 joules is usually adequate for 20 to 50 acres. Lightening strikes can damage energizers. Surge protectors and lightening arrestors are recommended to minimize energizer damage.

Poor grounding is the leading cause of electric fence failures. An electric fence must be properly grounded so that the pulse can complete its circuit and give the animal an effective shock. It is important to follow manufacturer's instructions for grounding electric fences. A minimum of three ground rods should be used for each energizer. It is estimated that 80% of electric fences in the U.S. are improperly grounded.

An electric fence is a psychological barrier rather than a physical one. Animals must be trained to respect electric fence. Once trained, they should respect the fence even if it is off for any reason. A voltmeter measures the charge the fence delivers and is an inexpensive but useful tool for trouble shooting electric fence problems.

Electrifying one or more wires in a conventional non-electric fence will prevent stock from pushing through the fence. New fences will last almost twice as long if they have electrified offset wires attached to them. All single offset wires should be set at two thirds the height of the animal to be controlled. An electrified scare wire approximately 7 inches up and 5 to 7 inches away from the fence will give a coyote a strong shock and keep him from returning.

Temporary fences, also electric, go hand-in-hand with improved grazing management. There are various materials available for temporary electric fencing: light weight smooth wire, polywire, polytape, rope and flexible netting. Wind-up and reel systems are easy to move and install. Temporary electric fencing has the advantage in that it can be moved when weed pressure becomes too great on the fence. Cost and ease of use are the primary considerations when selecting temporary fence materials.

Non-electric high-tensile fence. A non-electric, high-tensile fence is constructed of the same materials as the electrified version, but more wire is needed since the strands are spaced closer together. Since the fence posts have to support more wire, more fence posts are also needed. A non-electric high-tensile fence is more expensive because of the additional wires and posts, though you save money by not buying an energizer.

A comparision of fencing costs
Type Materials Labor Machine costs
Woven Wire $1.20 $0.51 $0.17
Barbed Wire $0.87 $0.47 $0.16
HT-Electric $0.47 $0.27 $0.16

Here's a website that can give you an idea of what your costs would be.

http://www.maxflex.com/

Good Luck,

Dave

Premier in Iowa makes electric fencing specifically designed for goats. We use heavy welded "Hog Panels" for most of our fencing, and they work quite well. We chose the panels because they are easy to move, pose no danger to small children, and, because the "Hog Panels" have close spacing at the bottom, confine the kids as well as the adults. We still sometimes use the charged wires if the snow gets so deep they can step over the fences, but we no longer use it for routine fencing purposes

As already stated, get your electric fence in good shape. It sounds like you need a better charger. Solar power, battery powered, short mileage chargers, don't pack enough punch. Get a charger that puts out LOTS of power. The low impedence are great, but work best with tensile wire, not cheap or easy to install. For other fencers you need good solid wire, good grounding and clean fence wire without weeds or touching things. The voltage has to be able to flow around without interruptions. Goat should get knocked down if they touch it, even accidently.

Goats are a PAIN to keep contained, too creative. But getting a good electric fence, several wires high and at least 48", working well, should help a lot. Then you have to trim or weed kill the bottom regularly, to keep it clean of plants that ground it out. If goats are getting out, leaning on it, the electic is not getting thru well and must be fixed. Boers are worse because they are big and strong, make more trouble than smaller goats.

You are the goat's owner, up to you to keep them contained. That is the law.

I would be screaming too if I was the neighbor. You would not like my large horses running around in your yard! Or even my large dog trying to play with your goats, leaving havoc behind her. Everyone needs to keep their own livestock and pets at home.

hmmmmm this propably explains why my fence did not work a cheapo from Lowes cost $22 and did not last for crap! Fi-Shock Super 525 Electric Fence Controller. soooo yakimadn I went online armed with new knowledge and whaddya know I found some more high powered units that might do the trick.