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It's my understanding from reading a major (meta?)study recently that maintaining muscle should be as simple as working the muscles enough to activate a mechano-sensor protein like once a week should be enough. Basically weight lifting and maintaining that "pump" for the rest period between sets. I know that if you're not making gains, it's likely you're not getting enough protein. At least, protein is usually the first thing to double-check is more what I'm getting at. Followed by making sure you're working those muscle groups often enough, you're increasing weight/frequency enough, adequate sleep, adequate amount of calories, etc.
Im not a doctor, but I have a good few years experience in the gym, and my suspicion is that it may be diet related. You'd be surprised how often you need to adjust your macros and caloric intake, especially when doing the bulking/cutting method. If you're already at like 1 gram of protein per pound of bodyweight(while cutting? Doubt it), then I would see about adjusting the amount of calories. I know, super difficult to fit those macros, but you gotta adjust the diet to get the results you want at the speed you want. In any case, it sounds to me like you're not quite producing enough energy (as has already been suggested). Your body may not like the amount of calories cut per day and/or the amount of protein isn't adequate to maintain.
And one other thing is to keep in mind that you've been at it for a year, so it's common for people to keep plateau-ing in various metrics at your point. Even the usual adjustments can be much less effective at this point. The body is great at adaptation, and sometimes that can be counterproductive to the goals we're trying to attain.
In any case, it can be any number of things. I've had buddies in the gym plateau then suddenly start getting gains again by adding a little cardio, or fixing their sleeping schedule, or noticing they haven't been hydrating like they know they should. Hell, I've even heard of stretching as a "workout" on rest days working for some. If you get a good bit of the "obvious" stuff squared away (sleep, water, etc), along with double-checking your macros/calories and you're still losing strength, I would go see a doctor and/or nutritionist.
I should probably also mention that cutting and maintaining muscle is very difficult when doing the cutting/bulking method. It usually comes down to protein intake being inadequate because of the difficulty of keeping within caloric restraints. So most people kinda just accept that strength loss will happen when cutting, which is perfectly valid. Just depends on your goals and priorities.
Sorry, tl;dr: 1. Ensure adequate protein intake to maintain 2.Make sure the calorie reduction while cutting isn't too dramatic 3. Ensure adequate sleep/hydration for recovery 4.If you're sure you're hitting the above points adequately and still losing strength, probably talk to a doctor... which I am not.