How to properly caulk a plastic shower?
The most likely reason is that this specific caulk doesn't have good adhesion to the specific plastic. The problem is solved by using some other caulk - the best bet is to figure out which plastic you have and look for caulk that claims "adhesion to X" where X is your plastic.

I had a similar problem once - otherwise very useful Henkel sealant that adhered to tile so good I had to cut if off with a knife wouldn't hold on PVC window frames. I changed the sealant to the one that claimed adhesion to PVC and it still holds perfectly.

Btw maybe elastic silicone sealant is a better fit for the application you describe.