Jake,
just got back from my first trip out reliant on a canister stove (Coleman F1 Lite like yours).
We used it many times over the weekend, eventually finishing it at lunch on Sunday, and on several of those attempts it conked out mid-cook whilst there was plenty of fuel inside. The stove is new (well second hand bought from an OMer unused) and the canister was a coleman 100. I'd asked my mate to bring along a trangia burner full of meths just in case... and fortunately we didn't have to use it.
This is what I did (not a recommendation... just a comment)
Stove conked out... evidently the valve was open as it was burning perfectly up to this point.
Suspected problem with the canister... closed valve completely.
Waited a minute or so... burner still hot (especially the relatively large mass of metal above the thread for the canister)...
Held it with a piece of cloth & unscrewed the canister completely.
Re-threaded it... opened the valve... heard the hiss of gas & re-lit. No problem thereafter until the next brew! Repeat the process!
This was the first time I'd used canister gas; my 'main' stove is a whisperlite and I've often camped using trangias in the past - occasionally even hexamine blocks. I can't say I'm too impressed. The whole point of this was convenience for a dehydrated meal.
If this happens on a new canister, I shall be not amused. Perhaps I just got unlucky. Perhaps there's a design fault.