I'm beginning an RFI for a public relations agency to help with brand reputation / brand perception strategies. I've looked at the Gartner Market Guide, but it appears to be mostly large PR agencies. Any recommendations on mid-sized PR agencies?

A good midsized PR agency I've had a good experience with is Lambert out of Grand Rapids, MI. Experience in high risk industries and they do a great job of strategy and then implementing systems to manage reputation after strategy is defined. https://lambert.com/

Here's a few : 
- Red Lorry Yellow Lorry (specifically reach out to Meredith Eaton). 
- PAN 
- Touchdown PR 
- Axicom is a branch of a larger agency but more accessible

Yes, you'll only find the big guys in a Gartner MG. If you are looking for a smaller agency, then you can consult O'Dwyers. Look for agencies with experience in your industry. While you are going to need to avoid an agency working for a competitor, the expertise in your industry will help them fast track their reputation and brand work for your company. Location is somewhat a consideration if you feel face-to-face is important. However, I don't think being located in the same city, state or region of the country is that important anymore. There are excellent virtual agencies out there.

IGNYTE is a branding agency in San Diego headed up by Brian Lischer.  If you get the brand analysis right, then brand activation can be a turn the crank process with a competent PR agency.  But check with Brian first before you spend money on PR.

EJP Marketing or duGard Communications