For the most part, unless multiple monorails are out for repair, monorail service is reasonably predictable.
The MK loop is crowded at the start and end of hard ticket events. The start of hard ticket events can be surprisingly bad--as one group of guests are using the resort monorails to get back to their hotels as MK closes to them and another group are using the same trains to go from their hotel to the park. Side note: during MK hard ticket parties,
DVC pools near MK are usually very empty.
The MK loop is crowded from late November to New Years as people check out the gingerbread houses (probably less so this year, due to the refurb at GF).
The entire monorail system will be overwhelmed just after closing during major holiday periods. At MK, you'll know because you'll see the metal stanchions by the monorail entrance likely when you arrive.
This will be especially bad if there are special fireworks displays (New Year's, Fourth of July, etc.). If you leave after fireworks on one of these days expect to wait an hour or more for any mode of transportation. On the Fourth or NYE, I'd do everything imaginable to ensure I stayed at a resort that I could walk to (Crescent Lake for EPCOT or BLT, VGF or even Poly for MK),
But outside of this, I rarely see situations where a line for the monorail is more than 10 or 15 minutes. It happens, but it's rare.