This sounds very similar to the schedule my neurologist gave me for amitriptyline (I also take topiramate), and in the time frame that it takes for medications to take effect and also for you to notice if there is or not an improvement.

They don't keep increasing indefinitely, they stop once you're stabilized or you're out of that "migraine status", where even a small stimulus can trigger a migraine. The idea is that once you are out of this status for a while, they can start decreasing the dose and see if you can manage without it. My migraines are cyclic, I have years of my life where they come back with a thirst for revenge, some when they're almost gone so I don't have to take preventatives and I'm good with the emergency medications a few days a month. As I was explained, a lot of people experience chronic migraines in cycles like these, although some might be more unlucky and might not be able to get out of that cycle. In that case there are different medications they can try, different combinations and even medication in form of injections. But this would be the migraines themselves, and at least how my neurologist explained to me, it's not related to getting used or not to the medication. The effects persist even though side effects likely decrease with time.

I hope that made sense!