Is the Bitcoin network slowly closing down?
It could be that this host specifically is getting less connections, although that might not be the case.

There has been a similar drop in hashing power and stock price. The most likely cause of this is the lack of press-attention and a low amount of things you can do with Bitcoins. Another possible explanation is the increased usage of online-wallets reducing the need for locally running clients and therefore the total number of hosts connected.

Overall, no need to worry about the Bitcoin network closing down. In fact it seems to be about to grow faster again.

Some backing for my claims is here:
http://bitcoin.sipa.be/

Although it's hard to say anything from these charts