Although they do require you to sign in (once) when you start, that shouldn't affect the link to controller.
I aren't familiar with the P4 but would suggest trying the relinking procedure.
If that doesn't help the dreaded DJI support may be next step.
To be fair if needed the warranty replacement turnaround is quite rapid.
However it seems to be in the small print that they may replace with a refurbished unit to speed things up rather than looking at any repair or even looking at it at all.
If this happens do a thorough check through, it should be 'as new' if not new.