Best answer on when your nonprofit ought to send out email is to TEST. No two organizations are alike.  Therefore frame your strategy around a plan to test frequently.

Look at your data.  When do you get the highest open rates, click-through-rates, and conversions? I’ll remind you that your content also influences response.  Just be certain to consider all factors when analyzing results (i.e., content, offer, design, timing, frequency of mailings, from line, subject line, etc.).

Outside of that fundamental principle – testing and analyzing results – I read a good article in the May 2011 issue of Direct Marketing News with a few more specifics, “Trial and error determines best email timing strategy to maximize response.”

Key points, suggestions, and factors to consider as you determine when to send nonprofit email include (from the DMNews article):

When are you most likely to stand out in their email in box? It may not be an ideal day except that the volume of email is low and therefore you become more visible.

Understand your prospects, donors, members, and advocates.  When are they most likely interested in hearing from you?  What are their needs?

At what time of day and day of the week are people signing up for your email? That may be a good starting point for when you send out emails.

Link email analytics to conversions (e.g., donations, joined your association, etc.).  If the open time doesn’t correlate to when they convert … use the conversion time.  It’s more important.

Recognize that mobile is an important factor. How many subscribers open your email on smartphones? Optimize your creative to appear on these mobile devices.

Test.  Test.  Test.  And test over several months and years.  Use data to maximize response rates and conversions and your nonprofit email campaigns will yield exciting results.