Well I would stop using the maintenance plan in the first place. You can do
the same thing with DBCC DBREINDEX.  With so little info it is impossible to
say what the actual problem is but I would eliminate the maint plan
altogether as a start. Creating your own job will allow you to have much
more control over the process and hopefully get better error logging or
tracing of what is happening. If you look in BooksOnLine under DBCC
SHOWCONTIG you will see a sample script that allows you to only reindex the
indexes that actually need reindexing. This will reduce significantly the
time it takes and load on the server.  I doubt this is a SQL Server issue to
begin with but again it is impossible to say. Since this is a very resource
intensive process that uses lots of memory, disk and cpu it can affect many
aspects of the server. If there is an issue under load this is a likely
candidate to bring it out.