Well, yes, sometimes. Don't all children get lonely at times? Not 24/7. Not 365. Not enough that I think it is a problem. In fact, it is those days that they are feeling lonely that that homeschool MAGIC happens.
Before I know it, they are creating a game, making a movie, creating a dance or song, creating some sort of new project, intensely working on an existing project, thinking, reflecting, observing, TALKING to each other, baking, acting out a play, playing on the Wii, laughing in the other room together as they "clean", and, dare I say it...READING!
Loneliness isn't awful, you know. It can be the very impetus for creativity, innovation, and finding yourself!
Most parents don't EVER want their children to feel boredom or loneliness. It scares the parents or makes them feel inadequate or something. MUST FILL EVERY MOMENT!!! Some families will fill every moment with classes, lessons, games, computer programs, hand-held devices, ANYTHING to keep the boredom at bay.
I submit that it is that very thing that is feared, BOREDOM, that can spur a person, adult or child, to try new things, have a moment to think things through, or simply relax and unwind.
The kids have a nice group of friends, many individual friends, and plenty of other acquaintances that they know that their alone times are opportunities.
So, what to do about boredom?
I encourage you to reframe the concept of boredom, from something to avoid to something to EMBRACE and to see as an opportunity to think, to become, to observe, and to be BORED!