All recordings now "Sample offline" after 2-hour session

Hi folks. I recorded a two hour, non-stop improv session in Live with 5 stereo tracks but now all recordings are showing as "Sample offline" and I can't figure out how to fix it.

I've located the files. I've also made sure the project appears in Places within Live's interface. I've even tried dragging and dropping the files from an external Finder window into Live, but they still show up as "Sample offline".

Each of these files is 2.25 GB. Is it possible they're too large to be handled by Live in the normal way i.e. is there a cache setting I need to change or something like that?