The SK article in question is related to a situation when you have advanced software blades: AC/URLf, AVI, Ani-Bot, Threat Emulation/Extraction, Content Awareness - enabled in your security policy.
Connection persistence filed is related to the classic FW security policy, where decision is simple, and the question is - what to do with the connections in progress that are no longer allowed by the new security policy. If you re-match, then connections that are now disallowed, will be dropped.
Now, let's say, you are moving from basic filtering to AC & Content awareness. Both SBs require streaming. For ongoing connections that you allow through connection persistence feature, streaming will fail, hence the log alert.
The logic here is simple. Since building the full stream for ongoing connections is impossible, you can either accept them through the new policy (and alert about it), or drop, with up_rematch_accept_possible_action parameter mentioned in SK.
If you decide to drop, you are risking to break legitimate connections where stream is unavailable.