I didn't pull it off the board but I did set up an identical circuit on a breadboard and found the following:
Two pins together does power the relay but it sounds like a very lethargic actuation. It isn't as snappy of a sound as a relay with the other uCs.
A pin without relay does output 3.2V
When the pin is connected to the relay the relay is only drawing (or being supplied) 10 ma and the voltage drop is 1.8ish
The relay draws 17 ma when connected to the power supply.

It does appear for some reason the PIC cannot supply enough current for the relay. It is puzzling me because it is well within the PIC's capability and the other two PICs I have power it just fine.

I am inclined to just use a 1320 for the application but it leaves me wondering what I am doing wrong with the 1827.