I have lots of Agapanthus and have never had any bug problem. Have you checked the undersides of the leaves for any type of tiny eggs or bugs? Do you know what was planted in that space prior to planted your Agapanthus?

Hi, basillady. There was a tall cactus of some kind there; it was planted by the previous owner. It suffered some odd damage (skateboarders?!) so I removed it.

BTW, I did crosspost on this in the California forum, and have provided a link to pix, if you would be kind enough to take a look.

Those pictures are here
http://s256.photobucket.com/albums/hh199/kelpmermaid/agapanthus/

Here is a link that might be useful: OP's pictures

Thanks, jean!

The black tips look like frost damage. Is that possible? As far as I can remember this is not a frost-hardy plant.

I've never seen black tips here--they turn a light brown due to heat and drought here, or they get sunburnt when they get too much sun and heat. Every yard in the neighborhood has them (except mine).

Well, I know it's not frost-- I'm in coastal Socal. I see the brown tips around, but nothing like this. On the CA gardening forum, it was suggested that I should dig them up, divide them, let them sit for a while, then replant after replacing some of the soil. It can't hurt to try I suppose.