As I mentioned in the comments:
The thing about chance is that every occasion he can appear, he only has a 10% chance to appear. Yes, this means that he should appear at least once every 10 times, but "chance" doesn't make that guarantee. So it's a possibility that you've just been unlucky of late.
To elaborate slightly, what this means, is that every time he is eligible to show up, he has a 1 in 10 chance to do so. This means the game randomly selects from 10 choices: 9 "no's", and 1 "yes". That chance is fairly minimal, and is entirely legitimate that this can happen indefinitely. I.e., there is nothing wrong with your game.
This is not the same as "stacked chance". Some games use a system that have a low percentage of success, but with every failure, increase the chance of success. E.g., You may start with only a 10% chance of success, but when ever you fail, that chance of success increases by 10%. You still have the chance to fail, until you have failed 9 times, in which case you have a 100% chance of success. Fallout does not use this system.
Try levelling up the perk (This does require you being a higher level though). From the wiki:
The appearance rate is 10% for the first rank, 12% for the second rank, and 14% for the third rank.
This doesn't increase that chance by much, but it can help.
From my experience with Fallout 3, New Vegas, and Fallout 4, I too have experienced large "droughts" where the Mysterious Stranger will just not appear. Sometimes taking up to 24 hours of gameplay for him to reappear (spread over several weeks, making it feel much, much longer).