I have a pull subscription set but every morning when I check on it I have
the status "Agent is suspect. No response within the last 10 minutes". This
should not really be a problem if the replications was still running but it
is not. I have to start the pull subscription again manually.

Isn't there a way to automate this procedure?

You can try scheduling the agent every minute or so. But if the agent is in
a hung state or actually doing something
this might not work.

When you see the message agent is suspect, do you see any activity on the
subscriber? Do you get this message
when you are doing normal sync's or when applying the snapshot.