I bet you're pinching the tube between the tire and the rim, and not realizing it, latex is much easier to that then regular tubes. You need to cover the tube with baby powder then put just enough air into the tube to give it shape before installing.

I tried using latex tubes on and off over the years and end up going back to butyl. Latex flats just as easily which is contrary to what is told in the world of tubes, they are about as easy to repair as butyl but have to make your own patches, cost more, but they do feel like you're riding with about 15 to 20 psi less than you actually are, they also have slightly lower rolling resistance but you can't feel it but could be important if your racing.

The way I patch which seems to work better than standard glue on patches or glueless which didn't work at all (but are fantastic with butyl tubes) is to take an old latex tubes and cut 3/4" round circles for patches. Then use rim glue like Pastali which works better than patch glue, and wipe a thin layer of glue on both the patch and the tube covering an area slightly larger than the area of the patch, then press on immediately firmly and flat for about 30 seconds. Butyl patches will work but the patch material won't stretch when inflated the way the latex patch will and this is why a lot of regular patches on latex fail or don't last long. Of course you have to remove all the powder from the area of the tube you'll be patching so carry some alcohol towelettes.