Working with MTS files when I can't import directly from the SD card

I recently filmed a show and partway through it stopped being able to read the SD card and stopped filming. Because that happened abruptly the files that were recorded are likely partially corrupted and I when I plug the SD card into FCP (10.6) no files from that date show up. However, when I look directly into the files on the SD card, the .mts files are there and seem to be pretty much ok. I know that FCP can import .mts files directly, which is what I tried, but the video doesn't flow smoothly from one file to the next. There's like a split second of missing footage and a tiny click. The same thing happens if I first try to convert the files to another file. So, if the FCP import window can't see the files, is there some sort of trick or workaround to be able to import the file as a whole, rather than the 6 separate .mts files?

Thank you so much for any guidance!