What causes webserver unresponsiveness?

I have a D1 Mini WeMos ESP8266 board, running as a webserver over external IP and port forwarding so it can be controlled from anywhere.
Accessing it gets an html response that a browser displays as a webpage, with buttons that make it do things like toggle pins or in my case transmit an RF message. This is programmed using the Arduino IDE.

The problem I'm having is, it works as it should for a handful of commands regardless of how they're spaced out (meaning this is a number of commands issue, not a time duration issue), but then it just becomes unresponsive and times out.

I need suggestions on possible causes I can look into. Is it possible my internet provider is throttling the external IP access? Is there some sort of buffer that's filling up somewhere?

I need suggestions on possible causes I can look into.

Start with your code. Since you didn't post it, or define how you measure responsiveness, or lack thereof, we can't really help you.

Is it possible my internet provider is throttling the external IP access?

Yes, but that is pretty unlikely, unless you, and thousands of your friends, are trying to stage a denial-of-service attack.

Is there some sort of buffer that's filling up somewhere?

Not likely.