I am also experiencing that, but not until recently. I noticed it when I installed Roverdude's "Sounding rockets" mod and noticed the nose cone that contained a parachute fell off real easy, but when deploy had no drag what so ever to slow decent. Tried it on other parachutes and they all seemed really flimsy (as in they fall off going 200+ m\s) and seemed really low on drag (other than specific "Realchutes"), removed a few mods but couldn't find out the problem. going to try a clean install but I don't know how to redownload all my mods from CKAN without saving the mods and installing them from cache, which wouldn't fix my problem. I already removed the sounding rocket mod but it did not fix the problem.
Edit: I misunderstood what you said. You said you would lose the parachute tab in the VAB and SPH. I got that too but it was a few months ago. If you are using Steam just verify the game cache. Back up your 64bit .exe and the mono.dll you used to get 64bit on KSP somewhere else so you only have to drag and drop those back in. In steam go to Library - Kerbal Space Program(right click) - Properties - local files - verify integrity of games cache. If you got the game some other way, just a fresh install should do.
I left my original comment because I have yet to fix the problem and not yet willing to go in CKAN and write down all the mods I downloaded.