mid-2011 MacMini failure to complete bluetooth recognition

Old style keyboard with 2 AA batteries inserted - working fine for ages then started having difficulties being recognised at boot up. Replace batteries - fine for a day then repeat next day. Now recognises the keyboard's original paired ID but will not complete the link up. Wife's new magic keyboard-2 required just to log in of course, and having to use now. Bluetooth searching goes on and on without getting further. The general rules for re-pairing don't apply if no recognition to trip the menu for it. On High Sierra now and not planning upgrading OS. Have 16Gb RAM so is fast. Apparently can't run Apple diagnostic with this age of MacMini (mid-2011).

This is the second Apple keyboard to fail, the first being a wired one with only 1 year warranty.

Reluctant to give up and just buy a new keyboard without certainty of compatibility.