Are these old tapes that you're importing? If so, they probably have some errors that cause the separate clips. I have been working with a large amount of legacy footage recently (over 200 hours) and see this problem with Final Cut Pro also.
What are you using to import the footage? And old video camera? For starters I would get a head cleaning tape and use it as per the instructions. If you have not cleaned the heads regularly, that could be the problem. You might also try a different camera or video deck. Perhaps you could rent a professional video deck, or purchase a used one. They should be more robust than an old consumer level camera. However, individual cameras (especially cheap ones) can have their own idiosyncracies that makes it hard to import their tapes on another camera.
Also, what format did you use when recording the tapes? If you did not use the SP format (that gives about 60 minutes per tape) then you will probably have a lot of issues, especially with old tapes. You will also probably have issues if you used the longer tapes that could hold more than an hour in SP format.