Update 0.157.1 is currently rolling out. PvP should work again!
The remote PvP invite does not arrive at this moment.
But there is some workaround. Although not ideal. Battle through QR scanning does still work. Although it is not clear if scanning a friends QR using a picture on a secondary device works on a remote battle. [Now Confirmed]
If you are on an older version than 0.157.0, hold on, don’t update. Niantic is aware and promised the fix in the next version. I guess 0.157.1.
Ah, that’s why I couldn’t do PVP last weekend. Though I’m pretty sure I hadn’t updated it then.
Maybe your opponent did.
When he sent me a request it worked.
So it might be that 0.157.0 can send but not receive. 
Interesting.
Or maybe both have to send it…
That works. Friend sent it trough Whatsapp, then i scan that picture from the web app with my phone and we can keep battling. No need to resend every time.
That’s why I couldn’t do one this morning to get rid of a quest.
Remote Trainer Battle Invitations Failing to Send
From the known issue site:
Issue Description: When inviting a Trainer to battle remotely, sometimes invitations are not successfully sent to the other Trainer. This issue does not affect Trainer Battle invitations sent via QR code.
Issue Status: Fix currently rolling out
Last Updated: October 10th