I have the same problem on a 2021 MacBook Pro 14-inch (Monterey 12.1 - so doesn't look like it's fixed in 12.0.1).
Problem occurs for me when two finger scrolling. It randomly stops responding and keeping the fingers down and moving them around when it occurs does nothing. If I lift one finger then the mouse responds and if I lift two fingers and place down again scrolling continues to work (annoying when continuously scrolling down or up a page to have it stop randomly).
jgdavies
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For me this was caused by enabling low power mode. After disabling it, the issue went away.