After that, the frequency very much depends on your business. If you have regular offers or discounts, consider sending every time 2 or 3 have been announced. If the offers are on a variety of services or products then segmentation would be a great way to send frequently but not to everyone, segment your clients into lists of people who are interested in the different services, and email each group when the new offers are announced.
If you hold regular events, then you can think about emailing people plenty of time in advance to prepare for the event, and then again in the run up to it, to remind those already booked, and to encourage those last minute bookings.
Emails with advice can also be sent more often than straight sales emails, as your clients will appreciate the advice included within them, consider your business and see if there is perhaps a series of advice emails that could go out, over a longer time period, as people will then be expecting the next one.
Try subscribing to your competition and see how often their campaigns are sent, not only will this give you insight into your particular field, but may well give you some inspiration for future campaigns for your own company.
You need to monitor if your strategy is working, check your email metrics regularly, and over time, increase or decrease frequency and compare the metrics. Examine your open rates, click-through rates, conversions, sales, ROI and any other data which is specific to your marketing goals. Also measure responses, when you increased frequency, did the number of unsubscribes increase exponentially, or was it on par? Are the same people opening the emails, or is it different each time?
Keeping your promises is vital, if you said in the welcome email that customers will receive regular offers, make sure that they are getting them. If you start an advice series, make sure that you keep it up, leaving people hanging is a sure fire way to get them to hit the unsub button, or worse, just never open your email again.
As I said at the beginning, there is no set answer to the original questions, more a study on a case by case basis. Here at BrotherMailer, all of our account managers are experts in email frequency and will happily discuss your needs with you to find the correct answer for you.