First you need to find out how many days/mo. are required to give a rent increase. I would look this up for you but what if your county differs?
I am going to increase rent because my market will allow for it. I know I will not sit empy for long as the rental I provide is few and far between. Also I am way under priced by a long shot.
My lease is a term lease meaning if I say nothing the tenant must move out on X date. If I decide to offer the tenant another lease I have written in my lease that I will give 90 days notice. This is more than enough time for them to find another rental and also a judge will look at it that way as well.
So when the 90 days nears if I want to continue with the relationship I will offer to met the tenant to sign a new lease. If by chance the new term commences 90 days later and the tenant does not pay the new amount, that would put them in default of their lease and I would have to post a 3 day pay or quit notice. What would a judge say if I presented we just signed a new lease 90 days ago to continue with another year term, here is his signature, and now he is reniging on the agreement. No your honor he has not paid rent.
In each situation you really want to look at what you think a judge would rationally and logically say. I am not in a pro tenant state so I can count on logic to rule.
Like the other poster said you should really look at the other rentals in your neighborhood and determine where your price stands in comparison. There is a certain amount I would need to raise my current rent to the next tenant to make up for losing time if this tenant is unable to afford to pay the increase.