I was recently searching for a way to bypass the 3 time limit per year, and I've found one. Not sure if this is commonly known, but I wasn't able to find anything like it while searching the forums.
- Navigate through Xbox.com, and get to to the live chat option to speak to a customer support agent.
- Once connected to the agent, make up a story about how a relative would like to play the games you have digitally purchased, but your account has already reached the limit of 3. Also make sure to say that you had no idea about the limit of 3 per year. (Not sure if this can be done by simply just asking for a reset, but I did it by making up a believable story)
- They will say they're sorry to hear about your issue and that they can reset it.
- They may ask for confirmation on your account, so just go ahead and give that.