bflyer,
that is not quite correct. TCAS will display an aircraft with a transponder turned on. Even in Mode A (so you don't get any height read out from the target, just the target displayed). The TCAS II systems talk to each other in a RA, so that they both don't climb together or both do descend together. You will even get an RA in response to standard Mode C equipped aircraft. I had one recently sent off by a cherokee. Now as TCAS II is in the region of $300,000USD plus, I doubt the PA28 would have had it fitted!!
TL,
My guess would be, that at a particular relative alignment of the two aircraft, the your lower TCAS antenna was line of sight blocked from the lower aircraft's transponder or TCAS antenna simply due to the close proximity and much greater angles.