Very long time to first byte

[capeinfo]

Hi
On one page, I repeatedly have a very long time to first byte. If you look at http://www.webpagetest.org/result/120105_W6_2RH59/,
First view: 85.5 secs (first byte: 76.3 secs)
Second view: 9.9 secs
Third view: 4.2 secs.

The home page shows a similar story (http://www.webpagetest.org/result/120105_50_2RH84/):
1st: 52.2 secs
2nd: 4.5 secs
3rd: 5.6 secs

The site is Joomla with a JAT3 template which minifies, combines and caches files. This slowdown is recent and I just can't pinpoint what might have caused it.

Any idea what might be causing this?

Thanks
Carl