POP3 servers don't like concurrent access, and since mail checks in AquaMail are locked to wall clock, they hit the server at the same time.
Please use AquaMail settings and set a "time reference point" on one and only one of the devices, to something like 00:02. This will offset this device's mail check schedule by that much. The setting is in global AquaMail settings, under Mail, receiving.
Now, Gmail.
Their IMAP server has a server side limit of 10 IMAP connections per account, counting all devices, all mail apps. Each folder in push mode requires its own connection. Also, when the device loses connectivity, it takes Gmail around 5 minutes to nice and cross out that connection.
Solution - reduce the number of folders in push mode in AquaMail (and maybe in your desktop mail app, if it uses IMAP IDLE / push mail).