I couldn't pay February's rent but have maintained my rent payments before and after.
I am now paying an extra $100 every month on top of my rent payments.
They are still threatening to take me to court and evict me.
Don't I have any rights in this matter?
What ever happened to 10% or $10, whichever is more? Is this not still acceptable?
I have now paid 1/2 of the amount owing and they are still threatening me.

Please advise.
Thank you

$10 dollar or 10 percent ? You are joking, there is no law like that, that is a myth and was not about rent anyway.

They could have, and still can evict you at any time. Normally in book keeping the way it works, if you did not pay Feb, but pay in May, the money paid in May is for Feb, so you are paying late each month. And they can of course add late fees each month, it would be easy to owe much more a 100 dollar extra may not even be paying the late fees.
Depends on your rental agreement.

Yes they may evict you if you do not pay the full amount due when it is due.
They have only been very very nice up to this point.

Thank you for your response. I realize that I'm being treated very patiently, as they are not adding more late fees... just the original $34.
I have to say that I honestly thought I had rights here because I've been here and paying on time since September of last year. I just had a hard time in Feb. In fact, I had the money in my NEW account and they still took payments from a cancelled account, which bounced and cost me large in bank fees. They were given the new banking info 3+ weeks in advance.
Originally, they agreed to an extra $100/mo but today they said that they never agreed to that arrangement.
Still no rights for me?

Nothing you have added makes any difference.
I have no idea what 'rights' you think you have, whether paying on time for the last 5 months prior or the last 5 years.
And now the story isn't making sense, because you say you had the money in a new account when you owed it, in Feb. If it was there, why didn't you just pay it as soon as you realized they tapped the old closed out account? And settle the costs of bouncing then? Do you have proof on paper that you gave them the new account info (a separate matter entirely; it won't stop eviction).
It sounds like they don't believe your need to pay $100/mo and that you were juggling bank accounts and hiding money or something.
Tenancy isn't cutting off heat in cold weather or land line telephone when you are elderly. You only have rights when you pay the rent in full on time.