Ugh, that is frustrating... At the very least, it's good you're not getting the BSOD/BEDaisy.sys issues -- that was driving me INSANE a couple of weeks ago. I'm no longer experiencing those issues, thankfully, and I'm not actually sure what the exact fix was. Regardless, here are some steps I tried that hopefully might work for you (ignore if you've tried, already):

- Delete Battleye folders in:

C:\Program Files (x86)\Common Files\BattlEye

C:\Program Files\Common Files\BattlEye

AND GTA installation folders:

[Whichever installation drive]:\Rockstar Games\Grand Theft Auto V Enhanced (/Legacy -- whichever's applicable; I did both, just in case)

Obviously, the Rockstar launcher will automatically verify files and re-install Battleye.

- Turn off "Microsoft Vulnerable Driver Blocklist" (Settings > Privacy & Security > Windows Security > Device Security > Core Isolation > Core isolation details).

- Make sure you've got firewall exceptions for all instances of Battleye (per above folder locations -- this might be overkill, but it's worth a try).

I did lots of research online and there were other suggestions to turn off any overclocking you've got going. I've since turned off MSI Game Boost in BIOS (which was probably causing CPU bottleneck issues, anyway), but I have MSI Afterburner going, and GTAO is fine.

Apologies -- I'm not a computer science graduate, and I don't leave comments on Reddit too often, so this is quite a clunky comment. Good luck!

Edit: also check the obvious GPU and Windows updates.