Sounds like some serious CPU throttling going on. Could be one of two causes:-
1. Thermal Throttling caused by excessive heat. Verify this by using software like CoreTemp/HWMonitor, running your game in windowed mode and checking the temps when the FPS tanks. Thermal Throttling is a legit cause for concern as your laptop may not have adequate cooling. Alternatively,
2. If it's not the temps that are excessive (and I'm assuming you're plugged to the wall socket and not running on battery power), then it could easily be the Mobo that's responsible for this throttling phenomenon. Some manufacturers like Dell like to place these artificial throttling mechanisms to prevent excessive power draw (underpowered power bricks could be a factor), preventing both your CPU and GPU to work at their fullest potential after a certain period of time, which I find absolutely infuriating, as your laptop is not allowed to run at it's rated capacity.
The only ways to solve this issue (that I know of) is to either update your laptop's BIOS to the latest one, or use software like
Throttlestop, which will allow you to bypass the throttling and let your machine run at full capacity 100% of the time. I can vouch for Throttlestop personally, as I'm currently using it for my own 4.5 year old Dell XPS Studio 16 laptop which had this issue from the start (it was a systemic issue present in all laptops of that line, and the symptoms exhibited were the same like yours)
Just make sure excessive temps are not the issue first before using Throttlestop. It's pretty potent stuff.