The weak link for flash drives is usually the USB connection. Original USB was/is pretty slow. USB2 is quite a bit faster, and USB3 is a lot faster.
The controller in the computer has to be able to handle the faster ones, and if the controller is old you won't get anything faster than what the controller can handle by using a flash drive that meets the later specs.
If it's a connection speed problem, the file transfer will stop when you overrun the buffer capacity in the computer.
An option, if you have the hard drive space, is to record to the hard drive, and you should then be able to copy from the hard drive to the flash drive without hitting any connection speed problems, since the computer can vary the "read" rate to accomodate a slower "write" capability of the flash drive.
The flash drives themselves can be formatted in various ways. Older ones were often pre-formatted as FAT16 which can impose a limit on the maximum size of a single file. FAT16 can't handle an 8GB drive, so you can assume a drive that large won't be formatted that way.
More recently, nearly all flash drives have been formatted FAT32 or NTFS, either of which allows much larger single files; but you still may hit a file size limit less than the full drive size. I haven't been able to find specs on whether there are real single-file size limits for either, but without better information you should probably consider, as a possibility:
The total size of the drive doesn't necessarily mean you can write it all in one file.
Some of the earliest flash drives were observed to have "problems" if you tried to reformat them to a different kind. I think that difficulty has been overcome with more recent ones, but I haven't seen comment that specifically says so. You might want to check with the maker of the drive you're using for instructions about reformats.
USB is a tremendous improvement over the older serial port, but it is possible to run into "port corruptions" if you've used several USB devices, especially ones that are connected and disconnected fairly often. The recommended procedure for cleaning things up (in Windows) is to disconnect "everything USB" then go to Control Panel and "delete all the USB ports," reboot with NO USB DEVICES CONNECTED and connect the USB devices back one at a time to let the system rebuild the port setup. Unfortunately, it's impossible to find a mouse or a keyboard in my locale that isn't USB and I haven't figured out how to do a clean reboot without at least one or the other. (This isn't very likely to be your problem though.)