Because you use it twice a year?
That infers you may have a partial tank of gas sitting for months at a time, going bad.

Air filter- "Looking clean" can be misleading. Spring for a NEW one. it's only a few $ and eliminates any possibility of the old one being clogged with "micro" particles.

The battery is probably bad from age.

Sorry - I should have been more specific Yes, I use a brand new air cleaner at each use. Also, the gas i use is fresh from from the pump the day i use the mower and at the end of each use I run the mower out of gas. The starter motor is new in 2013 and the battery is new in 2010. The battery was tested in 2012 and found to be 100% capable of delivering its full rated amperage and voltage. it is stored indoors when not used and trickle charged with an automatic battery charger during mowing season. The mower is covered and is stored in a shed when not used.

is this equipped with the automatic choke?

It has a bulb primer. I should also mention that the carb is not adjustable

If the battery was tested in July of 2013, it could be meaningful. NOT 2012!
A new air filter every time you use it? That doesn't even sound logical?

What's the model & Type numbers of the engine?
Assuming it's a Briggs 12H807-1775, it's a fixed jet engine, so the only way it could run rich is a clogged air cleaner or leaking needle/seat assembly in the carb. That latter could be cause by "fixing" the carb and not flushing the fuel line before reattaching. it's VERY easy for a tiny bit of crud to get washed down to the needle and prevent it from closing all the way.

Bill - thanks- sorry for the delayed reply.

I know it doesn't sound logical but,yes, I replace the air filter at the beginning of the 2 uses per season - just to make sure I;m not "choking' off any air flow.. The fuel line is new (synthetic 1/4 inch fuel line SAE standard ) and installed in 2012 - so there is not much chance its causing a problem. The battery i was just tested again and found to be delivering its full rated amperage and voltage after being charged by the alternator, I'm curious now about the needle and seat you mentioned - I don't think i have ever replaced it. Do you recommend replacement?

Thanks again for your response

IF the needle was leaking, the fuel level in the carb bowl would be high, causing a rich condition.

My 20+ year old Honda has a "sooty" looking plug whenever I pull it, but it has no indication it runs rich. I think it's a nature of unleaded gas that we don't have the "gray" coating.

About the only hot starting issue I can think of is a heat sensitive coil (armature).
You might check spark when cold and then again when hot to compare the quality.

Thanks for all your input