UPDATE : IPv4 monitor has the same issue as the IPv6 one.
I thought it would, mine usually look broadly similar.
I'm stuck... I can only think that either:
a) tbb and AAISP pings are being handled differently by your router (seems pretty unlikely!) or
b) there's something odd on the part of the route to you that tbb uses and AAISP doesn't. Which seems equally unlikely, so there's probably a third possibility that I haven't thought of
How often do AAISP ping your router? Is it possible that the brief periods of packet loss are "sneaking between" the pings?