You need to use the Grenades/Items option for special weapons. The only one that seems to have an issue with it is the Hydra Launcher. For some reason the gun will just not reload at all, other than that the options work for me as they should. As for the no reload option I have not used it much, but the few times I did it worked fine (but again not with the Hydra launcher but that seems to be a problem with the gun itself).
It only works for the timers for the main mission, not the challenges.
i have been having that same problem.
I also can't get the explosives on the bridge to ignite when the convoy is driving over it and I keep having to restart that mission over and over.