What can cause access to the mail server to disappear?

Question

Mail server

Good afternoon. There are 2 rooms, Internet from 1 provider, but 2 different routers and 2 dynamic ip (all devices in room 2 and connected to router 2 have identical errors).
In room 1, everything works stably, in the second room access to mail (send a message or even log into a user account) is periodically absent, while the Internet works flawlessly. The reason for the shutdown is not clear, sometimes it restores work itself. Let's say they left on Fri - it didn't work, they came on Mon - it works all day, on Tue it works until 9 am and turns off until the router was reconnected (it helped for 20 minutes), software restarting the router does not help. The client - Thunderbird, when it did not work, tried to download other clients - it did not help. Mail does not come through the web interface. I reset the router settings, the provider says that they cannot do anything that will create this problem. I tried to change ports in the client, security methods (SSL / TLS) - nothing helps. The mail server pings even when the mail is down, so it's not about him,
This router has 18 PCs + phones, MFPs. There is a client on the phone, I switch to wi-fi from 1 room or to 4g - it works.
Error, by the way: "Error sending message. The message was not sent because the connection to the outgoing mail server (SMTP) "mail domain" timed out. Please try again
" seems to be nothing out of the ordinary I
see only 1 solution - change the router, but there is no spare and it’s not a fact that it will help, but just buy this
upd1: the provider said that you need to contact the mail server with this problem and tell them that we have 2 gray IP behind NAT. 2 gray means room 1 and room 2.
upd2: connected another router, while we observe its work

Answer 1

From the task it is not clear how everything is configured,
1. Do both rooms have a common network?
2. In the screenshot of the DHCP logs, if item 1 is correct, then you have 2 DHCP in the same network?
The phrase "(the rooms include all computers that are connected to the router, the errors are identical for all)." read several times, did not understand.