For the last couple of weeks, I've had a weird issue with BATC.   I don't use a mic, I use the menu system to communicate with ATC.   I used to get an immediate response from the AI ATC (unless another aircraft was talking over me), now, I select my message but it takes a minute or two (or longer) for the message to go out.   It then takes the AI folks in the tower just as long to respond to me.     I still get ATIS right away but for any of the other ATC functions, it's just one delayed response after another.    Any idea what the issue is? 

It is a problem. Apparently the devs are aware of it. 
 

https://www.avsim.com/forums/topic/678082-very-slow-beyound-atc-response-times/

I’ve done a few flights over the weekend, and I didn’t notice any long delays getting a response. Maybe some transient server or network issue?

Been a problem of and on the last few days, reported on their discord. Server issue on their end I guess.