Sounds pretty much like the battery - make sure the voltage is high enough when using a Lithium/diode mod. The voltage drop from the diode might make the battery seem empty rather quickly.
I replaced the battery with a fresh new NiCd one - and will replace it every couple of years.
Another choice is to replace the battery with a NiCd or NiMH one, but rather then soldering it directly to the board you use a pair of wires to put the battery where it can't do much harm - preferrably in a closed box. Be aware though that your Miggy might not be stored horizontally all the time in the future.