It may be that you have it set to MP4 recording format and stops once it hits a storage limit.
If you set it to "AVCHD", you can keep recording for as long as you have power and/or memory space.
AVCHD produces mts files and one mts file should be enough for a song without the need to do anything else to it...but if you record for an extended period of time (like a play, event, etc.) the recording gets broken into separate mts files that need to be joined together on your computer into one file (later/after recording done) with either the included Pixela software that came with the camcorder, freeware tsmuxer or editors such as Sony Vegas, Premiere, etc.
Once the card is in a card reader or connected to your camcorder via USB, if you navigate through the folders, the mts files (all you need) are located in the STREAM folder.
This is not unique to your camcorder, with most current camcorders this has to be done. The files will still be there but to have continuous playback as one file, the individual files need to be joined together.
BTW, these Canon camcorders don't run risk of overheating such as the case with something like a T2i DSLR camera.