"My HSA bank has never reported my monthly fee ($3) on a 1099-SA."
Could it be that you pay for the HSA from a credit card or direct deposit from another account or something other than you HSA itself? My HSA fee is deducted from the HSA itself so I believe it would have to be considered a distribution. (?)

The bank deducts its $3 fee each month from the HSA. I do not pay separately.

My bank has this statement regarding fees and taxes.

"If administration fees are withdrawn from the HSA, are the withdrawn amounts treated as taxable distributions to the accountholder?
Amounts withdrawn from an HSA for administration and account maintenance fees will not be treated as a taxable distribution and will not be included in the account beneficiary's gross income."

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The fee is not a medical expense but it is neither a distribution taxable to the recipient. 

You go on to state " I have received a 1099-SA with distributions totaling those fees"  

The advice is the custodian has filled out the 1099-SA wrong and reported those to the IRS as distributions. The custodian needs to provide a corrected 1099-SA.  

You have to followup with the custodian.

If the custodian refuses to correct the 1099-SA get that information in writing from then and you would need to retain the supporting documentation that they are refusing to correct the 1099-SA.. You could then paper file using your corrected distribution amount(amount not including the fees) and include a letter of explanation why your box 1 reporting to IRS is different from the custodians. Clearly state that the distributions were fees taken directly by the custodian and were not distributions made directly to you the recipient, (Account statements would support those were taken as fees and not distributions) and are expenses not to be reported in box 1 of form 1099-SA as distributions. 

azandyman is correct:

"The fee is not a medical expense but it is neither a distribution taxable to the recipient. "

 

If the custodian is UMB, when you call UMB, the response you're likely to receive is you need to call ConnectYourCare.  When you call ConnectYourCare, they will tell you to call UMB.  Do not fall for this trap!  From the beginning, inform UMB the monthly maintenance fees are not a distribution, and you will not waste time making another phone call.  Tell them to document this information for a supervisor, and you want a supervisor to call you back after they have corrected the 1099-SA.  Also ask them when you can expect a call back.

 

The first time this happened to me, I wasted a lot of time calling UMB and ConnectYourCare because both refused to take ownership of the problem.  The next time this happened, I sternly told UMB what they needed to do, and not to waste my time.  I placed a call to UMB on a Wednesday, and was told I would get a call back within one business day.  I got a call from a supervisor on Friday that they had issued a corrected 1099-SA with a gross distribution of zero.