At the point where the tape stops, take it out and flip the cover up. See if the tape is physically wrinkled or damaged. That's probably what's stopping it. When you forward and rewind, the tape isn't wrapped around the head drum and into all the rollers, so the machine wouldn't complain when you're doing that.
Assuming that's the problem and you feel brave enough to get into some basic video tape surgery, you might be able to repair it. Unwind the section of tape onto the table. Put hopefully a single piece of scotch tape on the back of the damaged video tape section. Ideally, you should try to get scotch tape that's the same width as your tape, or at least very close to it. If it's wider, then you'll need a steady hand to trim the lateral edges. If it's thinner, you'll need a steady hand to trim the lateral edges after you've carefully applied the scotch tape as upper and lower halves.
If you need pictures to illustrate the procedure, let me know.