Is Splitting Monthly Rent a Fair Housing Violation?

[Jody Schnurrenberger]

I've had a tenant for nearly a year now and I love her.  She keeps my place like a show home.  My rent is high for the area ($1400).  She is late with rent sometimes and I'm worried that she might move because it's too expensive.  It took me 6 weeks to find her (because the rent is high--that's a long time in my area) so it probably won't rent quickly if she leaves, plus I doubt I'll find someone else who keeps the property like she does.  

I want to offer her the opportunity to pay half rent at the beginning of the month and half mid-month, to accommodate her pay.  I suggested this to a friend with a similar situation and it's working out great for them (nearly a year now).  However, I mentioned this to a property manager today and she said this would violate the Fair Housing Act if I didn't offer this for all my tenants.  

But no one else is ever late and it would be a headache to keep up with if everyone decided to do it, so I don't want to. What about if my tenant asked for the accommodation? Would this break the Fair Housing Act if I do it for everyone who asks? I could have someone suggest she ask, or is that a problem, too? It's a SFR and I don't own anything else in that neighborhood. If anyone cares, it's in Auburn, Alabama.