II typically send the message, wait two days, send a reminder, wait two days, and then act on whatever the case/ticket concerns if I still haven't heard from them. So if you check your email less than twice a week and we need something from you, you're boned.
Personal rant:
For most professions, it isn't necessary to have your phone or browser constantly notifying you of new emails, but in any field using email as a main form of communication, if you can't find the time to check email at least three times a day, you aren't someone I want to work with. (I've actually had to let someone go because they refused to make a habit of checking their email).
Not counting the few addresses/labels I allow to notify me right away through mobile or browser, I check my email roughly twenty times per day (every working half hour). But with all the amazing features of gmail combined with my (now) effortless priority labels, I usually spend less than an hour a day actually working with email. Anything time-insensitive that needs lengthy/delicate wordcrafting gets delegated to overnight.