Just to keep you up to date.
I tried a new cell in the remote, no change.
I tried a slightly slower 2Gb card, it didn't get better or worse.
I tried the AI Servo suggestion, but on switching to manual focus the AF box on the display goes blank.
I tried the manual trigger at the 3 second interval, I got to 55 shots before I got a honey can you do....
I tried my 40D with the remote, no problems, would still be clunking away now if I didn't stop it when it got to 100 shots
I tried switching the IS off, no change.
I tried Av and Tv modes, still paused at 25 shots, ie no change.
Tried with the battery fresh off the charger, no change, didn't get to try with the grip.
Didn't get to try a longer (5s) interval, but the manual trigger works ok.
It sounds like you've definitely narrowed it down to the camera. It sounds to me like its filling the buffer and then stopping while it writes to the card. It really should not be doing this.
Its not for certain that its not just a limitation of the old camera design, I sold mine many years ago. As cheap as DSLR's are right now, I'd upgrade to a 40D. Mine went on sale on Ebay yesterday, it was the 5th one I owned, but when I took some product photography photos of bright red hats a few days ago, I ran into the old issue of how the reds are over exposed on many Canon DSLR's, and after shooting with my 5D MK III and comparing the reduced for web shots, there was a huge difference in color accuracy and in resolution even though they were only 1024 X 1024. Now, I'm using the 5D3 for that, even though I did not buy it for that purpose. I might buy a refurb 70D tp replace it once Canon starts offering it on the Canon Loyalty Program for 20% off the refurb price.