This happened to me as well, and I thought I wouldn't be able to complete the game. The icon for the inventory would disappear, and even if I had already selected the remote before climbing down the ladder, the remote icon would disappear as well. I played around with tweaking the game settings and eventually was able to play through without the inventory/remote icon disappearing.
I don't know if this will work for you but this is what I did: changed render setting from Remastered to Original, turned Advanced Lighting to Off, and via the shortcut, enabled Compatibility Settings (checked the box) and selected Windows XP Service Pack 3.
Not sure what fixed it for me but I think it was the compatibility setting. I had to play around and try with a few different ones to find what would work. After playing through that scene, I went back and switched to prior settings and didn't have any further issues. I had used this fix twice in the game -- to get past the Ocean scene (game would crash before cut scene) and the alligator part. For what it is worth, I am playing on Windows 7 64 bit and my PC is above the minimum requirements listed.
I hope this maybe helps you. Good Luck!