In America I would tell you to take it to Best Buy. The connector is obviously loose or dirty, and with a hard drive for a computer there are ways to remove it from a case, and/or connect it other ways, even taking the disk and installing it in another drives reading device. A flash drive is solid state, and is hardwired into the connectors at the end. If even one of the connectors becomes loose, or even really dirty, it will stop reading. If the files are valuable enough, try getting an electrical connector cleaning spray, radio shack might have some behind the counter they could let you use, and try cleaning the terminals. Make sure it is specifically for electrical connectors, there are types that will clean it without leaving any residue.
Pushing the terminals into, or pulling slightly to align them may work. Frequently the cause of the terminal disconnection is either being removed at angles from the port, or being forced into an unnatural angle while plugged in. By wiggling the connectors, you might get it to register one last time to get what you need off.
One last thing, have you tried plugging it into any other computers? There was a case I went through where somehow the drive label for :e drive got disabled in the computer, and anything plugged into it would get assigned to :e and would not show up on the computer page. I assume you have tried different ports on the same computer, so I doubt your computer port is the problem, but just in case…