How often is communication lost with aircraft?
According to this FAA paper, Table 3, ASRS reports were analyzed for 16 months between 1978 and 1979. This included 553 incidents where the recipient was not monitoring, which seems to be the closest category to loss of communications. This equates to a little more than 1 incident a day. Note that this only includes incidents that were reported, and air traffic has increased since then.

This report contains info from ICAO in in Europe. The focus is on the security issues from unresponsive aircraft. In just the northern region, there were 230 flights over just 6 months in the beginning of 2004. This number inclues airlines, business jets, and military transports. This frequency is a little higher than the previous report, but is more recent and probably includes less flights.

Other reports like this one don't include a time frame for the reports analyzed, but look at other factors involved. For example, pilots with fewer hours and GA pilots are more likely to be involved in such an incident. The average duration of these incidents was 7.6 minutes.

This page also has some good information about this type of incident, including a list of some of the many possible reasons for lost communications and excerpts from some of the reports.