Well for the first time ever, we don't have to have a two-week long discussion about when do do the competition, thanks to our planning for the year and future.
Competition #11, a.k.a. the 2017 Spring Competition, will be starting on Friday, 26 May 2017 (the start of Memorial Day weekend in the USA) and ending on Sunday, 25 June 2017.
Note that while this is a 1-month competition, running through the Spring and upcoming Summer Competitions, as well as the time between them, will compose a single 100-day period of time for making a game. In other words, the start of this competition is also coincidentally the start of a 100-day game dev challenge for those who want it.
While these are the official dates of the competition and what most people will be using, you should feel free to bend the dates a bit to better suit your own personal situation. If your weekend is Wednesday and Thursday, feel free to shift the dates by a few days. If you've got a bunch of tests at the end of the school year that you need to concentrate on, feel free to delay the start of your competition work by a bit (or just do a 21 day competition instead of a 31 day one).
Remember: the real goal of the competitions is to get each of us into a pattern where we can weave game dev into our busy lives. You shouldn't have to put your life on hold to make a game, nor should a busy life completely prevent you from doing something you love like game dev. Find the balance that works for you. That's the true purpose of these competitions.