You may have to go back in this thread a bit, but people certainly have had this problem. The problem is that not all airlines actually use First Middle Last as separate fields, and some offer a field for Middle name when booking, then don't actually use it on the ticket. Generally, if you book FirstMiddle (in First Name field) Last (in Last Name field) and don't use the Middle name field when booking it seems to work. My issue happened on LH (and is somewhere upthread) where I had to book the ticket with "Joe Robert" in the First Name field and "Smith" in the Last Name field (sticking with the example show by others in this thread). Basically, non-US airlines don't seem to care about middle names. I will say I was surprised by mahasamatman's comment about one airline merging the Middle and Last names.

The problem you have with COPA is likely that she didn't end up with the ticket booked with any part of her middle name. UA won't like you/her changing this often, so the better strategy is to leave it and book tickets in a way to ensure that UA MP will actually validate. Using the 24 hr cancel policies is good here. If she books a ticket and enters her MP number, she should be able to see if it took in a short period of time. If not, cancel and rebook with the name in a different manner. As noted, when she has a middle name in MP, she should book tickets on non US carriers using the FirstMiddle method.