To address the question - no, you do not have to get him off. You don’t have to do anything at all if you don’t want to, and don’t let him force you to do anything.

However, I know this can be frustrating for both parties. My wife has extremely long periods. Sometimes they last 15 days of longer. I don’t get upset with her because I know she can’t help it - and I know how miserable she is for having to be on her period for that long. She’s seeking medical help, and it’s getting better, but it still happens sometimes. I get frustrated because I want to have sex with my wife, but we can’t. I have known this for a while, and I could have easily left if I wanted to, but I didn’t. So what we do is have sex a lot during the times when we can. When she’s on her period, I masturbate. She doesn’t like giving blowjobs, and I wouldn’t expect her multiple times while she’s miserable on her period. I’ve learned to deal with it, and I love my wife enough to where I can overlook this inconvenience.

Your boyfriend is in a similar situation. If you are saying you can have 2 week long yeast infections sometimes, then you have a period that lasts a week, that’s 3 weeks of no sex in a months time. I get it, it’s frustrating. Just make sure you’re getting as much medical help as you can. Second opinions and all that - just make sure you’re doing your part to prevent them from reoccurring. Next, you need to have a serious discussion with him about this being part of who you are, and that you need to reach a compromise. The compromise being (if you’re okay with this, obviously) that you both have sex a lot during the times you don’t have yeast infections, and then he can masturbate when you have them. Explain to him that there’s nothing you can do about this situation, and he needs to love you regardless of lack of sex due to a medical condition. If he doesn’t agree, then it is time to seriously consider ending it.

Best of luck, and I’m sorry for your situation because I’m sure it’s miserable.