If you have a specific problem, it would probably be more helpful if you ask a specific question. There are many, many types of formats that an avi can be. But for regular DV, a one hour tape will create a 13 gig file, if you record the whole thing as a single file. On older PCs if you have your hard drive set up using the old format (fat32) there is a 2 gig limit on any file size. The solution is use a hard drive with NTFS format.
I regularly play and edit files which are several hours in length. These files are mostly DV and HDV, although I use very large intermediate files which are compressed with HuffYUV, Lagarith, Cineform and MJPEG2000. Some of these files are well over 500 gig in size. I haven't noticed any problems related to file size or length.
It's certainly not true of modern computers in general ..
The size can be limited by the operating system, the file system - FATxx, NTFS etc..
Also, some applications may have file size limitations. You would have to refer to
the specific application ..
The file size could be large due to format as well as length. DV files are about 13GB/hour, but an uncompressed AVI of the same material will be about 107GB/hour. My system can play back a 450GB DV file just fine. It can't handle a 1GB uncompressed file very well and the playback frame rate will drop to about 8fps. Uncompressed HD slows my system down to about 0.5fps. Of course, i can still feed an uncompressed file into Vegas and render to some other format from it just fine.