Stacy, it can very much be related to CF for a number of reasons. A good place to start is an overnight in-depth sleep study (there are a few different types of studies so be specific). That will identify a few things. #1, if you do or do not have sleep apnea. #2, if you don't have sleep apnea, it will identify the # of times you wake up completely during the night, as well as the number of times you come out of the REM level of sleep into one of the previous levels (i hope that makes sense). Even if you don't completely wake up, anytime you come out of the REM level (because you cough, have some chest congestion, delay in breathing but don't have sleep apnea...) it is disruptive to your sleep and can cause fatigue because although you may be in bed and "sleeping" for 8 hours, you may only be in the REM level for 4 of the 8 hours, whereas someone like me (I don't have CF so no congestion, no nighttime heavy cough...) is in that REM level for 7 of the 8 hours that I am in bed.
We discovered that was my husband's problem. He was in bed for 8-10 hours a night but his sleep study showed that he awoke completely about 5 times a night, and came out of REM about 30 times. When it was all added up, he was only getting about 3-5 hours of REM sleep-hence his fatigue and need to nap all day long. The doctor recommended treatment of sleeping pills (since it was not breathing related). Good luck with whatever you find works.
Julie (wife to mark 24 w/CF)