Lossless with gaps

Perhaps the problem is with your player?  I don't have any experience with aiff files but all my MP3s, OGG and FLAC files play gaplessly without issue on my PCs (I use Foobar), my iPod Touch (loaded via MacBook Pro / iTunes) and my iMod (with Rockbox).  All of my MP3s and OGG files have been transcoded from my FLAC files using dbPoweramp.  I swear by their ripper and converter and have used it for a number of years.

Another possibility is the source of where you got the music.  You said these are downloaded CDs.  Do they play gaplessly when, say, you play them through your computer?

We need a bit more info to help diagnose your problem.  Gapless playback is a high priority with me since so many of my CDs have tracks (not to mention the entire CD) that blend one into the other.

So you have tested the original files and they play fine.  Hmm... not really sure where to go from here since I have done exactly what you are doing (in regards to MP3s) with no problems.  I'm assuming when you transcode that you don't have any added options in dbPoweramp set.

The only thing I can offer is explain how I do it and see if there are any differences with your steps.

I typically use the batch converter since I tend to transcode multiple ripped CDs.  I select my FLAC files then go to the actual converter and set up for MP3 (I usually use the -V 0 setting).  Set my output location to dynamic so it builds the directory via the meta-tags.  No added options are selected and then execute.  Import the MP3 CDs into iTunes, let it process then sync it to my Touch.

The above works for me every time.

Have you tried transcoding to yet another format and play it?  If it is still messed up then it must be something with the original file.  Another test you could do is rip one of your own CDs to FLAC and go through the same process.  If no problems then the issue again points back to the original file.

That's about all I can think of.