i have the tivoli gm and it doesn't sag at all. i've had it for 2 yrs now. probably doesn't sag because i use a chameleon purse organizer. i use the organizers in all my bags. not only does it keep my things organized, but retains he shape of my bags, including speedies.
I have the Tivoli PM and it doesn't really sag. There's a very slight sag when it's not full and the items are heavy, for instance, but I don't have any major problem with that. Definitely won't go as saggy as a speedy.
I've had the Tivoli GM since it was first released in 07. It sags a little and I bought a base shaper specifically made for it (on ebay). IMO, it loses a lot of it's beauty and charm when it slouches & sags, even if only a little. With the shaper, it keeps its shape just like in the advert pics and keeps me happy .