At work we keep connection counts below 10 for productivity so there is no router I know today for such high counts. Not that it won't work. Even the 20USD router "works" but as you see there are troubles as the count climbs.

Only a seasoned tech would know that 802.11n has but one non-overlapping channel and that many devices don't work well in a crowded area. They may drop and reconnect which you accept in an airport but not at home.

For this I'd pull back to 802.11g and field a router then a WAP to split the herd so to speak.

No one would be able to warrant a single access point to handle that many devices without issue.

There's so much to know about this that I can't put it all in this space.