That is quite unusual. A cuke plant can have more than half a dozen fruits, at various stages at its peak. BUT if you leave one or more too loo long (for seed or by accident), then it might shut down.

It is likely that your growing conditions are not up to par.

I give it about 1" of water a week and fertilize with fish emulsion + kelp.

It started off as a weak plant after it was attacked by slugs and wilted under the heat. But it survived and is producing 1 cuke at a time and continues to grow taller everyday.

I was just wondering how I could get more cucumbers off of it simultaneously.

First: Where are you located ? What are daily high/low temperature? How many hours of sun ?

Second: Generally speaking , I inch of water per week seems to be not enough for cucumber plants. I would easily water them twice a week.

Third: Best way would have been to have riche fertilized soil at planting and the supplement . At this stage, cucumber can benefit from any balanced fertilizer, or some with slightly rich in Phosphorous(for fruiting).

What color are the leaves : light green, medium green, dark green ? . You have to read your plants.

I'm in sacramento, CA. Highs have been in the low 100's and lows are in 50's. 8+ hours of full sun for this plant.

The cuke was planted as a start and it was planted in fertile compost with an organic slow release fertilizer.

I attached a photo of the newest cuke that's growing with the surrounding leaves.

I'll start watering twice a week.
What's a good organic phosphorus fertilizer?

Thanks for the help.

Hi uscjusto

First off, your plant look just fine.

I think, it can use more water(in triple digit), as I said before. I inch of water per week is probably not enough. Then one inch over how big an area ?

I would fertilize it with PHOSPHOROUS rich (poor in Nitrogen) fertilizer, the so-called BLOOM BOOSTER type. After all, you want fruits not foliage.
P.S.
Another reason, your cuke is not producing is because of heat. Do you see some blossom drops? But, if your soil has good drainage, water them more often.

The long, Asian type cukes do seem to produce fewer but larger fruits. That said, the advice here should help you get more production than one at a time.