I'm curious as to why you think not raising the rent reflects badly on me? I raised it by $25. the second year they were there. They always paid on time and I enjoy being a hands-off kind of landlord. All my other tenants have called me when they have leaks. I've asked when it's time to switch over the air to heater how things are going, any leaks, etc. They were just a messy, dirty little family who grew out of my little rental and moved when I did raise the rent. I couldn't really have done anything differently.
If the market you're in is flat and you are charging market rents that's one thing. if the comps do not support a higher rent then you are doing the right thing in not raising rents and losing your tenant.
Inflation moves upward no matter what,....each year. If you allow your rents to stagnate they fall too far below market and it is impossible to catch up.