Mark on "[Plugin: Jetpack by WordPress.com] WordPress Site Continued Access to Jetpack Management"

The security waings are simple ones from WordFence plugin telling me that a plugin needs updating. It does this when there is an update available for that plugin. It monitors the website and was me by email if there are any problems or conces, like updates.

I usually leave the 1st waing for a day or two, to allow Jetpack to catch up, but when I get another waing (2-3 days later), I know there was a disconnection with Jetpack for that website. I go in to find that either the WordPress account connection was changed to another WordPress account I manage, and of course, the update does not work, or the connection was lost and have to reconnect.

I am trying to figure out what I am doing that changes the connection to a different account so I can avert this problem from that aspect. - IS it possible that if I enter one WordPress account for one client's website, then close without logging out, then open a new tab, log into another Clients WordPress account, that this causes the previous website connection to shift to the second account?

As for the disconnection, I have no clue since you say that once the connection was made, I do not need to remain logged into that WordPress account for JetPack to update.

I do not manage these websites in my WordPress account, I create a separate WordPress account for the client and access their account. This because if my management for that client ends, they have they own account to work from.