This has been a major problem with digital television for me, so I'm glad to see it mentioned.
Some good potential solutions have been offered (i.e. manually keying individual frequencies to attempt a search), but my experience with digital televisions has shown that the engineers did not really consider real-world usage when they made the scanning modes, especially for fringe locations. My own tv, a "Westinghouse" model did offer a "custom" scanning mode in which you could choose to just scan a certain range of frequencies. This was cumbersome to use, but worked well since it didn't throw out anything outside that range whether or not it found new channels or not. Unfortunately, the tv screen turned magenta (apparently a common failure mode with LCD screens as I've experienced 3 of them) and required warranty replacement. The replacement was a newer model, but it had NO custom scan (and no program guide, wtf?). I have tried manually typing in analog frequencies, but have thus far had no success in adding new channels without a complete rescanning. You cross your fingers and hope that you don't lose channels. I've found that each brand has its own tricks in order to obtain new channels, but in my experience none of them are actually designed with directional reception in mind. It's a shame, really, because while digital broadcasting brings many benefits, the switch has shown that electronics manufacturers no longer understand how people actually use their off-air televisions. Unless you get by with an omni antenna OR all your channels are in a single direction, the tuners are a pain to live with.
I will add as a sidenote that the digital tuner in my replacement television does perform better than the one in the original. It's not all good, though, because the new tuner will blank entirely in harsh conditions while the old one would still show choppy, artifact-laden scenes, but overall it's an improvement because it picks up channels which the old tuner never managed to detect at all and generally offers more viewable channels than the old one did. Neither of my Westinghouse tv's have had useful signal meters, though, so I can't recommend the brand. My point is that tuners have improved even on off-brand equipment and I hope that manual/custom scanning feature will also continue to improve as companies relearn the art of off-air broadcast television. This is an extremely frustrating reality, however, since you pay a lot of money for a modern television and usually only later find out how well the tuner and scanning modes are designed.
<rant on> My reception could be improved by buying/building a higher-gain antenna, but my channels come from a number of compass directions and thus I don't want more directivity simply because my television tuner would require constant rescans. I just put up with marginal reception and regular blackouts on certain channels rather than improve my reception. What good is an antenna rotator when the television has to be rescanned each time you rotate? It is actually difficult to compare retail or DIY antennas when directivity is considered, because the design goal is usually the highest forward gain. I know that less gain equals less directivity, but unless the very generous people on this forum post 3D "flower" charts for a range of frequencies it's hard to know which antennas best fit my needs. I guess I should be willing to experiment more instead of wanting easy answers

. <rant off>
Please continue to post ideas and/or tuner brands that are better for directional scanning. It may be helpful to know for those in the market for a television. Thanks.