If the dropouts are generally random, the heads are probably just getting clogged with debris after running for a while, which will vary greatly depending on the tape. If you seek a complete copy of a long program, I think it's far easier to replay the dropout areas, get a good playback of those areas, and splice them back into the main file. What's the alternative, keep playing the whole hour until it doesn't dropout somewhere? Making splices is a good skill if you are going to do such work, and it's only a couple per hour. The machine is probably fine, but it may have head, wear, poor error correction, or debris in the guides or transport that move around during use.
Having other machines to try is highly recommended. I use cleaning tapes only as a quick cleaning measure when I start to hear a few small dropouts and need to finish something. Sometimes, only a deep transport cleaning will fix things, such a a tape that completely clogs heads and a cleaning tape does nothing. I can't recommend it without careful training and proper tools. I'm doing this at work (university music school), and have about 6 players to call upon, and in the last 3 years have done about 1,000 DAT transfers dating from 1989. I'm not willing to experiment with the computer drive method, but the ordinary method does take a lot of time to do right.