An interesting piece by Lawrence Booth @ Cricinfo on how public interest in country cricket is far higher than memberships and attendances at grounds might indicate. But i've suspected that for years, the main reason people don't go to county games is because they are on while people are working and so you don't get into the attendance habit. Despite being a Warks fan since my yoof after watching the escapades of Asif Din and Andy Moles on TV i only started going to county games (and a year later becoming a member) once i had a job with sufficient annual leave for me to be able to go to the ground now and then.
Weekend cricket has been tried of course, the Sunday league used to be very popular (like T20 now) but county championship games on a Saturday are generally not that well attended even if its not the last day of the match. The reason for this i think if again, people work in the week. The weekend is a precious time for them to do the things they have not been able to because of the 9-5 like shopping so again its hard to fit cricket into that.
Hopefully permanent floodlights (if we ever get them) and day-night test cricket may see some county championship games go day-night, it would be interesting to see if it brings in the cricket-hungry but time-poor fan. Though in mid-Summer you could probably play until 8pm without floodlights anyway.