Welcome to the forum and thanks for the post. Are you noticing wifi drops at other times or is this only happening when connected to the BT Sport app?
I had a few of these errors yesterday. It happens just with the Android BT Sport app. WIFI is fine otherwise. The WIFI signal was showing as max when the error occured. I simply hit ok and then the "watch" icon and it connected again.
It may be related to the Auto-Lock problem. Go to Settings/General/Auto-Lock and set it to Never. Worth giving it a try.
Have just had my attempt at resolving this with BT.
Was told that it was my devices. I argued that it was rediculous to suggest that two iPhone 4s would have the same problem.
Works fine on Macbook Pro and iMac over Wifi.
Obviously a problem with the APP.
Will have to wait for an update to ever be able to watch BT Sport on my iPhone it seems.