Mab25 - you've rec'd some first rate responses here, detailing why such a letter would even be required........
I'll just add my 2 cents worth. All income, to be considered eligible for your transaction, needs to pass a stability test: It must have been rec'd for the past 2 years, and be expected to continue to last for 3 more years.
This is obviously your sticking point in your transaction. I do find it somewhat unusual that your employer, or HR dept, would get hung up on this and put your loan at risk for observations/opinions that the underwriter could care nothing about. The lender is simply looking for this document to add to the file for CYA protection. Though this letter might seem ridiculous to the HR contact person, and possibly to you, I can assure you your underwriter sure doesn't feel this way.
I suggest that you try to find another supervisor who might be willing to write this letter and move on with your loan!
best of luck to you!