Unfortunately, I'm in a position where I plan to take a GMAT for a 5th time.
After my 4th test last month and considering whether to take it a 5th time, I called up a few schools to hear their view on multiple GMATs. I called Tuck, Fuqua, Booth, Johnson, Darden, and Ross.
All said they will use only the highest score for evaluation. However, they said that they will have access to all my old scores and may try to understand why I took the test so many times. Booth specifically said it's a red flag for them when they see candidates take several tests in quick succession (one in Feb, then in March, then in April, and then in May).
Several said that though the average is 1 or 2 times, they've had applicant's who have taken it 4, 6, 8, and 10 times. They didn't say whether these applicant's got admitted though. A few also suggested that you use the optional essay to explain why you took the GMAT so many times.
My own take away is if you think your current score does not properly reflect your abilities and you think you can realistically perform better (not just get lucky), taking it again is acceptable. However, I do feel, all thing being equal, a candidate who took the test once or twice will be more favorably looked at than one who took it 4 or 5 times, assuming similar scores. You just need to weigh that against your hopefully higher score.