I typically defend two arguments against an infinite regress of sustaining causes. The first is deductive. The regress of sustaining causes at any finite period of time is either itself finite or infinite. However, it would take infinite time for an infinite regress of sustaining causes to cause anything at all. Therefore, at any finite period of time, the regress of sustaining causes is finite.
The second argument is inductive, or probabilistic. If all of the known attributes of X are finite, and Y is an attribute of X, it stands to reason that Y is most likely finite. Since the regress of sustaining causes for any finite object is an attribute of that finite object, it follows that the regress of sustaining causes for any finite object is itself most likely finite.
Perhaps the objection to these arguments I hear most often is that between 0 and 1, there are infinitely-many points. Therefore, concludes the objector, an infinite regress can and does obtain within a finite object and/or finite period of time. The immediate response to this objection is that once all of the points between 0 and 1 are added up, the sum is a finite number, which is disanalogous to what the objector is purporting to demonstrate. Moreover, the points between 0 and 1 are arguably abstract, and not concrete, so one is not permitted to beg the question is favor of their concrete reality without additional argumentation.
Today, as I was listening to a 70's mix I had made a couple weeks ago, it occurred to me as I would turning up the volume that I could also turn the volume down to the point where the music would eventually be muted entirely (0 dB). Let's say, then, that at a relatively loud rock concert - roughly, 100 decibels - the volume is turned down progressively. Between 0 dB and 100 dB, there are infinitely-many points that correspond to a certain decibel level. Yet from this, it simply doesn't follow that there is an infinite regress. After all, the decibel level is bounded at 0 dB, which is a decibel level that is possibly obtained. In order for there to be an infinite regress, at least in any relevant sense, there should be no smallest decibel level; but since this is manifestly false, it follows that the regress is finite.