Despite my natural preference for researching from books (a quirk I share with BtVS's Giles), it turns out that the Internet is the place to go for information about my little problem. There's even a term for it - reverse cycling, and it's common when a baby hits the three month mark and becomes a distractible baby.
So I'm going to try some of these suggested fixes:
1. feed Baby in the bedroom with the curtains drawn so that it's relatively dark and boring for her
2. borrow a sling, and feed Baby in it (it should block out distractions)
3. keep trying to feed her at frequent intervals during the day (so she doesn't have to catch up at night)
4. find and wear what's called a nursing necklace; a necklace consisting of interesting-looking beads so that Baby has something interesting to focus on while she feeds.
I think I'll try 1. and 3. first because they don't require me to go shopping.