liamkk, welcome to WebmasterWorld.
Does losing the Google Plus box mean anything for the site
Was this a Google+ box with a map and then company info below that? I'll assume it was, and I'll make a few guesses here, but they are guesses....
One initial top-of-my-head thought suggests that maybe you need to update your url somewhere in your Google+ account to https.
Also, and this is even more of a guess... back in July-August Google had a major change in its local/map rankings, unofficially called "Pigeon", which conceivably might have affected Google+ pages in the Knowledge Graph type listings. Conceivably, a url change at just the wrong time might have put a listing in a queue to be reprocessed. It's not an area I've been watching closely of late, but here are some threads that might relate...
Pigeon Update Or Rollback Happening Now? July-Aug 2014 http://www.webmasterworld.com/google/4692003.htm [webmasterworld.com]
Pigeon was complex, and I posted in the above thread about why I thought results were taking a while to settle down. Whether this might have affected a Google+ listing for a site that had gone http to https is very hard to say....
I see the various factors... business type, map, named-location-in-query, IP-location, GPS-location, Google+ page, along with organic factors, all functioning like gears that need to mesh... but because of the different data sets, among other things, they're clearly not meshing yet.
Also see this thread in our Local forum...
Google "Pigeon" Updates Local Search Algorithm July-Aug 2014 http://www.webmasterworld.com/local_search/4690773.htm [webmasterworld.com]
Was the spike related to some Pengiun testing or pre-release or fine tuning of Panda 4.1?
Regarding Panda/Penguin, I have no idea what the spike and drop might indicate. We've got a lot of Google activity going on at once, and my thought is that to some extent that might be intentional. It certainly makes it hard to pin down individual factors.
I'm guessing that the spike was monitored by Google and was likely a test. You might want to analyze what happened to the traffic that you got during the spike, to see if it provided any clues about what possibilities for improving site engagement during that brief time. What have you been doing, btw, to improve the site since Panda 4? Google has dropped hints that site improvements might speed up recovery for some sites, even prior to running the updates.