Jar lids popping several times

It sounds to me like the seal on the lids may be very slightly compromised. For example:

• lids start down with a good seal
• pressure can't escape and starts building up like usual
• imperfection in lid seal gives way a vents out pressure/heat, lid pops up
• jar/contents starts to cool, constricting, again like usual - this is what seals the jars in a normal procdure
• Lather, rinse, repeat

Edit

A thought occurs: it's equally as likely, if not more so, that the opposite of what I described above is happening: i.e., the stock is cooling down and contracting, which creates a negative pressure on the jar, sealing it. However, in a similar fashion to the above, a slight imperfection in the seal holds to a certain level of pressure but gives way past that threshold, allowing the pressure to equalize (which causes the top to pop up).

If they settled in the lid-down position after they completely cooled, they are probably okay (note the probably). What causes a lid to 'pop' after it cools is usually due to bacteria being sealed inside the can and/or compromising that can afterwards. Bacteria starts to eat the food, produces gas which expands and POP goes the lid, and your delicious canned food is no longer safe to eat. So if the lids stay down until you open the jar and the stock still smells okay, you're probably safe.

This happened to me the other night. This is the first time I noticed the lids popping up and down for a couple of minutes after being taken out of the pressure canner. I was processing chicken broth. The only two anomalies were that I had taken the jars out relatively soon after the pressure allowed (instead of letting them cool longer in the canner), and I accidentally let the pressure rise to 15 lbs before I was able to lower it to 10. 25 out of 26 jars ended up with a proper seal once fully cooled.

That just happened to me when I was canning chicken stock. It was like a symphony in my canner. I usually count the pops as they are popping. I only had 6 pints of stock and the all popped at least 4 times each. I could see the lids popping up and down. I noticed that the other people that replied to this question were also canning stock. It makes me think that canning only liquid may be the culprit. They have all sealed at this time, but I will keep a close watch on them for a few days.