I have a sump pump in the backyard that was replaced 6 months ago.
I had it wired through a GFI and it worked fine until now.
Now it trips the GFI after 20 seconds. Then will only reset for a couple seconds unless I wait a half hour to reset it. Then I can get another 20 seconds.
Anyway, the manufacturer is saying that it should not be on a GFI so they won't replace the pump.

Is this typical that it should not be on a GFI? Does the fact that it does trip the GFI indicate that there is a problem with the pump? Should that be a warranted problem? If I wire it without a GFI will it trip the breaker when there is a risk of electrical shock around the concrete sump basin? If not, is there some other way to auto-detect this hazard?

Try it without the GFI, bet it works. GFI is not used for sump pumps and it appears that's what the manufacturer is saying too. The breaker will protect a short but not a ground fault. Your concern is probably higher than needed and it should be just fine on a good three prong receptacle.

I have a sump pump in the backyard that was replaced 6 months ago.
I had it wired thru a GFI and it worked fine until now.
Now it trips the GFI after 20 seconds. Then will only reset for a couple seconds unless I wait a half hour to reset it. Then i can get another 20 seconds.
Anyway, the manufacturer is saying that it should not be on a GFI so they won't replace the pump.

Is this typical that it should not be on a GFI? Does the fact that it does trip the GFI indicate that there is a problem with the pump? Should that be a warranted problem? If I wire it without a GFI will it trip the breaker when there is a risk of electrical shock around the concrete sump basin? If not, is there some other way to auto-detect this hazard?
A 30 amp dedicated breaker located in the service panel should be sufficient for your needs.

A GFI is just asking for trouble, usually pump failure when you need the pump the most.