WASAPI (Windows Audio Session API) is the Microsoft attempt to write low latency drivers. While it's a bit better than WME/WDM drivers, it's still a lot more latency than true ASIO which bypasses Windows entirely.
The trouble with ASIO4ALL though is that it's not true ASIO. It's a wrapper that goes around WME/WDM drivers to make them look like ASIO to your DAW. It'll give you more control but still isn't as low latency as a dedicated ASIO driver.
I'm not clear from your original post whether ASIO4ALL is what Alesis gave you when you downloaded their driver or it's just what you downloaded to try for an improvement. If it's NOT what Alesis is providing, I'd go to the Alesis download site and see what their dedicated driver does:
Alesis MultiMix 8 USB 2.0
However, if Alesis is providing ASIO4ALL then i guess you're stuck with it. As you've discovered, turning up the latency/buffer size will get rid of dropouts but, of course, at the expense of, well, latency. If this is the problem you're in, there are a few things you can do to hopefully improve performance.
First, optimise your computer for working with audio. A bit of Googling will find you lots of sites with instructions. Just search for "Optimise Windows (your version) for audio".
Second, ruthlessly shut down everything running in background...especially wifi/net and anti virus software.
Third, when adding effects, make full use of the ability to pre-render effects so your processor isn't doing them all live every time. You can still go back and change things but this can help a lot.
Basically the fewest extras you have going on, the lower you can push latency.