The idea is... (for EXAMPLE.. not saying this is exactly how it really happens).
Bulk.. gain 10 lbs. muscle/5 lbs. fat
Cut.. lose 10 lbs. fat/5 lbs. muscle (so you end up after one bulking/diet cycle with 5 lbs. more muscle than you used to have, and 5 lbs. less fat).
Then you repeat.. until you reach your genetic potential. Any strength you lose is always easier to regain because of MUSCLE MEMORY (what that means is it is always easier to REGAIN strength you used to have, than build NEW strength for the first time).
So the answer is yes.. you can and SHOULD gain it back and get stronger. Just keep your protein intake high while you're dieting, no matter what kind of diet you're on!