In playing XI since launch with a Logitech Rumblepad, what you have described sounds like either, as someone already posted - you have run turned off (?X-keyboard?). Sometimes it just seems to happen on its own.
Otherwise, it sounds like your calibration needs to be reset. The simplest and easiest may is to take the batteries out (or unplug) and make sure that the controller isn't resting on anything which might be pushing the joysticks or any buttons. If the analog buttons are not neutral when the controller turns on, when they 'spring back' the values of those buttons will not be 0. Sometimes this simple reset will not work.
After extensive online searching, I discovered Logitech Rumble pads can be turned on while holding in the shoulder buttons: I cannot rememeber which (triggers vs bumpers,) I usually just try few combinations, or all of them. This performs a hard factroy reset, and has been useful to me in both calibration, and wiresless connectivity issues.