this is what i have experienced,

i run FFXIV on windowed(x1080) i got 2 monitors, now sometimes when clicking out of FFXIV to lets say Chrome to go to YG.com or something, when i switch back to FFXIV the window becomes non responsive for like 2 sec, then i get RED arrows on connection then green again and puff timers are off, this only happens if i leave the FFXIV window, if i stay on FFXIV window only it never happens

try this and see if this its what happens to you