They just might... But no one can tell for sure. The way you react to mental fatigue is highly personal and cannot be measured in any way by an outsider.

There are also other reasons why your score stayed in place. In your three months of study, did you thoroughly review your mistakes and understand why the answer is such and such? While my personal opinion is that practice is crucial to getting a good score on the GMAT, your understanding of basic principles tested is essential.

We shouldn't forget that we all have bad days though. Maybe your prep is running smoothly, but just had not such a perfect day which might impact your score.

It's hard to say what, if anything, you're doing wrong without more details. Simply spending time studying isn't sufficient - it's all about how you study. Be sure you're analyzing every problem you do, whether you got it right or wrong. For math, make sure you're doing every problem in the most efficient way (not always the way the OG explains it). For verbal, dissect the right AND wrong answer choices to truly understand how the testmakers write the exams.

On another note, it's not unusual for people with already-high scores to have difficulty improving. A 690 is about 90th percentile, and improvements at that level take a lot of effort. My experience has been that people who score in the upper 600s/low 700s are really good at the GMAT - but people who score in the mid 700s or above have "it" - a deeper understanding of the test, where they can write their own practice problems, explain questions to others, have instant recognition how to solve a problem, etc. It's tough to explain what "it" is, but you'll know when you get there.