fossil, this is an easy one (and your username checks out, grin :D)
These SIACs most definitely have an old battery. Old, but not necessarily often-used, batteries become "lazy", a process called "passivation". Check
http://www.spectrumbatteries.com/id6.html for more details. In SIACs, the effect is that while the initial feedback at CLR and CHK may work (partially supported by a relatively large capacitor supporting the battery), later punch feedback at controls can not be sustained by the battery and therefore the SIAC enters a "loop of death":
10: SIAC enters and senses AIR+ field at control
20: SIAC writes punch to internal memory
30: SIAC starts feedback, but voltage drops badly and the electronics go into a so-called "brownout", feedback stops
40: SIAC battery voltage recovers a bit, a "watchdog-reset" happens, the SIAC "reboots back alive".
50: GOTO 10
This loop rapidly fills up punch space. On download, if the competition software is restricted to reading, say, the first 64 punches, this SIAC can even be claimed to have missing punches at the end of the course. If the software has a license model that allows more than 64 punches only on premium licenses and locks up if more punches are read from any chip, this SIAC might result in a "denial of service attack", locking down the software for any further use. No no, of course this never happened, and additionally it's been fixed long ago, would you please look at this shiny gadget called a neuralyzer for me?
If, in other software, such mispunch verdicts do still happen, a download in SI-Config+ will often show the missing punches.
The passivation problem on old SIACs was identified as an aging factor separate from voltage drop due to heavy use and checked by the "battery test" station, therefore the relatively recent addition of the "change every 3, max. 4 years"-statement from SI.
TL,DR; please have the batteries on those SIACs replaced ASAP.