I recently had a similar "Too many simultaneous IMAP connections" problem while using Outlook 2016. I tried all the solutions suggested online for curing the problem but none worked for me. I eventually found that
the source of the problem was my using the Google Gmail app on my smartphone (Samsung Galaxy 8). My story below might help some -
read on for further details.
My business e-mail has been set up under a Google Gmail account since 2015. I can access my business e-mail directly via webmail (Gmail), but I rarely do. I have 3 separate PCs (Surface Pros, each running Windows 10) with Outlook 2016 running permanently.
Each installation of Outlook 2016 accesses my business Gmail account (as well as 2 x Exchange mailboxes). My PA and I also access my business Gmail account on our smartphones.
I had no problems until a few months ago. Specifically, I would get a dialogue box pop-up asking me to insert password. Then a message advising that saying "... IMAP
server wants to alert you to the following: Too many simultaneous connections (Failure)".
I learned online that the maximum allowable number of IMAP connections at any one time is 15. I could not find out anywhere
how many IMAP connections is used by each e-mail client (Outlook or phone app) but I could not understand why the problem should suddenly arise given that I have had the same number of e-mail clients (3 x PCs and 2 x phones) accessing the Gmail account for
several years without any problem.
Having tried, without success, all the solutions suggested in various online forums, I contacted Google support. Misinterpreting the details I had provided to them (in which I had told them I was using the Gmail app on the smartphones),
Google support said "I would suggest that you use the Gmail application from the Play store, as this does uses a connection protocol of it's own an not IMAP, hence you will free up some
(IMAP) slots". This prompted me to look more closely at the Gmail app on the smartphones, as the problems in Outlook only started at around the time when we acquired new smartphones - the Samsung Galaxy 8 (great phone by the way!). On our Samsung
8 phones, the default (and only installed) e-mail application was Gmail. I used the native Samsung e-mail app on my previous phone, and my PA's previous phone was an iPhone 6. So I removed the accounts on the Gmail app on the two Samsung 8 phones (can't remove
or even disable the Gmail app!) and installed the Samsung email app instead (available form Play store). Hey presto - problem solved! As I advised in my response to Google support "....far
from being part of the solution, I have determined that the Google Gmail app on the Android phones is actually the SOURCE of the problem!"
I hope this story might assist others in the same situation.