DSL connection dropping

I've switched from a cable-based ISP to a DSL-based one. I'm finding
that the connection is often being dropped briefly, not long enough to
require a new IP address, but long enough to freeze remotely-running X
clients. When I complain to the ISP, they blame the router (a Linksys
WRT54GL with the latest firmware). Is this likely? The modem is as close
as possible to the jack which is on a dedicated line. There are filters
on all the phones; these are on a separate physical line but the same
telephone number.

Bob T.