I don't download podcasts, instead I add the URL of the file into my playlist and play it that way, as a stream, but I've found that when I pause the podcast, if I pause it only briefly it works fine, but if I pause it for slightly longer (haven't noticed yet where the cutoff is), once I resume it will not resume from the paused position, but it will instead play the file over from the beginning.
A further problem (and this might well be the same problem) is that when I close WACUP and then restart it the next day, it will also not remember where I left off on the podcast when I paused and closed WACUP the previous day.