Financially it probably makes sense to sign a lease with these applicants rather than leave the property vacant for an unknown period, even if it means not collecting pet rent or additional deposit.My question is: Would you push the issue for the "service dogs" and make the applicants provide a letter from a medical professional? 

You might benefit more from looking at the experiences and investing habits of high function professionals like medical professionals, professional athletes and successful business folk in other time demanding fields.  

Medical is a good example as is Real Estate ( I just leased some space to a real estate brokerage).Once you get office leased it is much nicer than MF.

Real Estate Investing is all fun and games until you need medical insurance. 

I have some medical conditions that will keep me from continuing that job long term as it is physically demanding. 

Hubby and I will continue to work for now since both of us work in a medical field and hopefully wants to retire soon with passive income.

Make sure you lean on your MD status-there are some special loan programs out there for doctors purchasing multiple properties.

Surviving a medical crisis is a lot like that.Read here for one of the best Grizzly survival stories.

She is also under a very watchful medical eye. 

Does anyone own or operate a medical facility (as tenant or landlord)?