Can collections agencies sue if I am making payments on my credit debt?

Collection agencies will do just about anything in order to get that payment from your hands and into their playing field. However, it is not necessarily their fault as they are just doing their job for their employer who signs THEIR checks.

Most of the time credit balance collection agencies will not go through with a lawsuit even though they can. The only time collections will sue is when they know you have the assets to pay them but simply refuse to pay. The main thing is what it would cost to sue. If they can’t get any money from you, then why would they incur all of the costs to go to court? It's simply not a good business practice for them to sue people who cannot pay.
One suggestion would be to write them a letter requesting that you pay them a set amount each month. They will most likely accept whatever reasonable offer they can get from you. If they purchased the debt then they will be happy to make up what they paid by getting incremental amounts.