I don't see 13.1 listed as supported or unsupported yet on the matrix. I have noticed however when I go to add a 22.214.171.124 device I get "authentication failure to host" even though the credentials are valid.
Not tried the path of adding a device yet, but I used BIGIQ 5.3 to upgrade a pair of BIGIPs from 13.0 to 126.96.36.199 without issue - can also still interrogate them remotely etc.
I had no problem adding a 188.8.131.52 device to my BIG-IQ 5.3 system just now. You may be able to get some information out of the restjavad.0.log file as it attempts to discover the device.
13.1.X is supported in the 5.4 release that was made publically available December 27th, 2017.