Are you absolutely sure that they were kicked because they could not pay their plot taxes and that it's not that someone had manually kicked them from town?
Because from my understanding towny only makes you lose your property (It becomes unowned NOT for sale, which I'm grateful for because like Alba said you can hold property to give back to someone), it has never kicked a resident from my town because they could not pay.
If, of course, you don't want your residents to have to pay taxes daily you could do /plot set plottax 0 (With "plot" in "plottax" being replaced by "shop" "embassy"/etc. to set the plot tax for each type of plot).
But I really don't think it was because they couldn't pay taxes they were kicked, I don't think you can set towny to do that, only to lose plots. So I'm more inclined to think someone kicked them.
TA/Mayor can see when the day turns to a new one in the real world on the server who couldn't pay taxes and lost their plots. I'm not sure how to check that outside of just being there and seeing it in the chat, but it does show it in the chat when you're on and it occurs.