1. Whenever one begins counting, it is impossible to form an actual infinite by successive addition. (Premise)
2. In the order of sustaining causes, one must begin counting at each finite interval. (Premise)
3. Therefore, the regress of sustaining causes must be finite. (From 1 and 2)
In my estimation, this argument is bulletproof. However, it's not even the primary argument Thomas Aquinas appeals to in support of the finitude of the regress of sustaining causes. The first argument he defends may be summarized as follows:
4. No instrumental cause can sustain itself. (Premise)
5. If there is an infinite regress of instrumental causes, then the regress as a whole cannot sustain itself. (Premise)
6. Therefore, there cannot be an infinite regress of instrumental causes. (From 4 and 5)
Thomas offers the example of a hand moving a staff. The staff is merely an instrumental cause, as is the hand. Without a first cause of the staff's motion, we're left with an infinite regress of instrumental causes, in which case nothing would ever be in motion. Since things are in motion, it follows that a first cause of motion exists.