Advice needed for overdue rent.

[Chris Harvill]

I have a tenant who is over due on her rent and need a little advice.

A little backstory on this:

She is in a 2 year lease that expires 7/1/15. She has been consistently late but generally paid monthly 15 days late up until October of last year. My first mistake was to let her get about 2.5 months behind. Finally in December we worked out a plan to get things caught up by paying every 2 weeks with an additional amount added in order to pay all past due rent off by the end of the lease. Begining in January she was paying every 2 weeks per the plan. April 1 rolls around and I received a text that her utility bill was exceptionally high and she needed a little more time. I told her to double up the 15th. Today, still no money and she is telling me she is trying to come up with the money. She is a school teacher and gets paid on the 1st and 15th so there is apparently an issue with her finances.  

My question for some of the more experienced folks is this:

Should I go ahead and ask her to leave and start the eviction process or shoud I try to get what I can out of her through the end of the lease?

My concern is if I evict I won't get any rent for the next 3 months. If she stays I may get at least part of it. This is my first property and my first lease so I am still learning. I definately will not let another teneant get this far behind again.

In advance I appreciate the advice.