So the Twitter site says:

Pagination and IM are currently disabled. They’ll be back.

…and lo! hovering over the “Older” button pops up a message:

Twitter is stressing out a bit right now, so this feature is temporarily disabled.

Wanna make bets over how much of that stress is due to folks hitting “reload” repeatedly?

I’m not sure there’s an easy solution, but I’m willing to bet that the load has shifted elsewhere by this means.