If the photo posted by @transistor is accurate it represents a Class 2 transformer with a center-tapped secondary.
Since it's a Class 2 with 50W out, it probably has a fuse internally. There are two common ways something like this could fail, and one uncommon one.
First, the cord could have failed - particularly the AC cord and usually near the strain relief or the circular connector. In the latter case, the repair is easy- open up the connector, shorten the cable slightly and renew the connections. In the former case you can usually open the case and push a few inches of wire through the strain relief and again eliminate the broken bit. If the unit works and doesn't work when you wiggle the cord at one end or the other, that is an excellent indication that a broken wire is the problem. Since it seemed to work for a while, this is quite likely the case.
If not, I suggest double checking with a multimeter to ensure it is actually bad. Test the primary and secondary resistances to ensure there is a reasonably low resistance (hundreds of ohms at most on the primary and probably tens on each half of the secondary) between the 3 sets of pins. If it measures open on the primary, it's probably a fuse. (If it measures continuity on all the 3 winding tests, plug it in and test the voltages at the output- if the voltages look about right- they'll be higher without a load- then the problem is not the power supply.
If it's inside the power supply, it can be opened- if there are screws, remove them and open the case, if it is glued or ultrasonically welded, you can carefully squeeze the sides of the case to force the joint open along various spots of the length. Look for a fuse inline- if you find one replace it (only) with the exact same type and rating. If you can't find a fuse, look for a lump in the transformer and maybe ask another question. It may be a thermal fuse. The fuse could have gone from getting tired (it gets a hit every time the unit is turned on and over time the element can sag and fail), or there could be something wrong in your mixer.
When the repair is done and tested thoroughly, replace the screws or epoxy the case back together.
The uncommon way- if you open the case and you smell strong burned insulation, then the transformer itself may be toast, and not practically repairable. That's rare though.