Ah, I know this one. Here's how; open MyCommunication.lua in a text editor (like Notepad, for example, that'll work fine).
At line 132, you'll see the following piece of Lua code, which runs when the addon is loaded:—
function mcoOnLoad()
ChatTypeInfo["CHANNEL"].sticky = 1; -- EM: As much as I like sticky channels, should we really be doing this in MRP?
if (not MTI_VERSION) then
mduDisplayMessage(MCO_LOCALE_MYTIME_MISSING_ERROR, MCO_NAME, .8, .8, 0, 1, 0, 0);
end
You can probably see the line that does the thing you asked about, because I placed a little note there myself when I took over maintenance of the addon, wondering about this very thing.

Place
two hyphens and one space in front of that line (the one that has
ChatTypeInfo["CHANNEL"].sticky = 1;) , and save the file. This "comments it out", meaning it doesn't get run, and the chat channels won't be "stickied".
This will not adversely affect the way the addon operates in any way.
After you're done, that bit of code will look like this:—
function mcoOnLoad()
-- ChatTypeInfo["CHANNEL"].sticky = 1; -- EM: As much as I like sticky channels, should we really be doing this in MRP?
if (not MTI_VERSION) then
mduDisplayMessage(MCO_LOCALE_MYTIME_MISSING_ERROR, MCO_NAME, .8, .8, 0, 1, 0, 0);
end
And then, once you've saved that out, MRP won't make the channels "sticky" when it loads anymore.
Is that OK? ^^