Heel pulling up out of shoe on the left only
 

My heel keeps pulling out of my shoe on hard climbs, only on my left. It doesn't seem to be too bad with new shoes, but with time, it happens more and more - I suspect that I'm stretching the shoes out somehow. Weirdly, it doesn't happen with my right foot.

Any advice on how to avoid this?

Check yer left cleat for wear. Might also be the crankset is loose, see if there is any lateral play.

Sounds like he his pulling out of the shoe, not pulling out of the pedal. This can happen because you are not pedaling smoothly, which takes more concentration on hard climbs. You can also try tightening your laces or straps more, but make sure your cleats are properly aligned to avoid twisting your knee.

your feet are two different sizes, everyone's are. tighten your left shoe more than the right

Try getting sole inserts and shims. You have one foot that's different than the other. We all do; some more so than others. Your local bike shop should be able to help you with this as it's a part of bike fitting (or at least it should be!)

^^^Like he said.

I find, in fitting shoes for customers that they never tighten the arch strap enough. They flick it a couple of times, walk around in the store and proclaim their heel is slipping. I reach down and crank the straps down and they look at me surprised. You might check that.

oops

^This... at least I know it's true for me.

Same with me too, but difference isn't more than 2mm.