Schengen visa duration of stay

I don't know what calculator you're using, but the official one works for 2017, and notes that if you enter on 8 May 2017, having your previous two visits in mind, entry may be authorized for up to 90 days.

Here, as requested, is an image showing the calculation. Note that the second visit constitutes 25 days, not 24 as indicated in the question:

An attempt without the calculator (basically, pay attention to the gaps between visits):

Assuming any earlier visit was before (not including) 31/3/16, by the end of the first visit shown you were present for 74 days out of at least 180. That's fine and allows re-entry.

By the end of your second visit, according to schedule, you will have been present 25 days (for the visit) after an absence of 100 days. To get up to the limit of 180 days continuous, 55 must be added, from the end of your first visit. 25+55=80 in total out of 180. That's fine and allows re-entry.
By the end of your second visit, according to schedule, you will have been present 68 days (for the visit) after an absence of 98 days. To get up to the limit of 180 days continuous, 14 must be added, from the end of your second visit. 68+14=82 in total out of 180. That's fine and allows re-entry.

You could increase the 82 to 90 by staying a further 8 days (though you might prefer some margin of safety), departing on July 22. By then you will have been present 76 days (for the visit) after an absence of 98 days. To get up to the limit of 180 days continuous, 6 must be added, from the end of your second visit. 76+6=82 in total out of 180. That's fine and allows re-entry. Yet usage (82 days) of you allowed 90 days is the same as above? That's because the rolling 180 days has moved forward and now does not include all of the time of your second visit.

At your third visit you could stay a full 90 days, since that would mean departure on 5/8/17 and counting back 180 days from then means that none of the time of your second visit counts (the 180 comprises the last 90 days out of the gap between your second and third visits, the 68 days you have planned and a further 22 days allowed). Hence the calculator showing the 22 day(s). However, the earlier you leave the earlier you would be allowed to return.

2016-07-15 to 2016-09-26: 74 days. You've spent 74 days out of the available 90.

2017-01-05 to 2017-01-29: 25 days. On 2017-01-09 you have been in the Schengen zone for 79 days in the last 180 days. This won't change until you leave. You are not overstaying.

2017-05-08 to 2017-07-14: 68 days. On 2017-07-02 you have been in the Schengen zone for 81 days in the last 180 days. This won't change until you leave. You are not overstaying.

As far as the daycount goes, you are good to go. We can't predict the rest, it's up to the border guard.