Of course the 120 day freeze on refugees and the limiting of refugee numbers to 50,000 in 2017 parts of the executive order will still be in force in October.
Since they are separate from the 90 day part that people apparently find the most objectionable and since the cases being dealt with by Scotus relate to the allegedly discriminatory nature of that part then those cases being moot by the time the Court comes back there is no reason for Scotus to offer any further ruling on any part of the order. It was partially reinstated today and that will likely be their last ruling on this particular executive order.
The Court will hear a moot case if the injury is "capable of repetition, yet evading review." I assume the defendants will argue that the ban will not be a 90 day one-time-only affair and that the issue could come up again under the same or a different administration and should be heard for that reason. Its the same reason the Court hears cases from pregnant women long after the pregnancy that set off the case ended.