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.