So the problem is the joint of the transformer wiring to the lugs. They may have cold solder joints, or the lug may be slightly loose - enough to crack the solder connection over time. Your transformer may still be good!
When you are examining the transformer wire make sure it is stripped enough to get good solder coverage. Burn off the insulation (enamel) - do not sand, scrape, or try to erode it because if you scratch the wire it will break at the scratch.
Re-solder the transformer connectors after first making sure the wire has at least two complete wraps around the solder lug and the solder makes a good meniscus joint to the wire and lug. Also use a good grade of solder, not regular 60/40, find some 63/37 solder (Kester is best) - this solder resists cold solder joints due to movement when cooling by solidifying very fast.
John :-#)#