Linked servers "Login failed for user 'xxx'. Reason: Not associated with a trusted SQL Server connection"

Hi everyone
I've read many articles about the scenarios where the error "Login failed for user 'xxx'. Reason: Not associated with a trusted SQL Server connection" usually happened. I think I understand the problem and the standard solution. Nevertheless I'm getting in trouble with this once again.
Here's the situation: I have a development environment simulating a customer production environment with a SQL Server 2000 (say Server2000) linked to a SQL Server 2008 (Server2008). Server2000 runs on a different virtual machine. Both servers have "SQL Server and Windows" authentication and the link is defined to establish the connetion with a login and password existing and working on Server2000.
In the logic tier, a windows service connects to Server2008 and executes some SPs which access some tables on Server2000 using the full four part name.
So far so good. As I just configure the link with SQL Server Managent Studio and begin to call the service, everything works fine. But if I turn the machines off and then on again (let's say the next day), I get the unpleasant error "Login failed for user 'xxx'. Reason: Not associated with a trusted SQL Server connection". If I change the account in the link definition and then change in back to the initial one (by means of SSMS), voila, everything works again.
The same occurs if I try to simulate some kind of problem, i.e. I pause Server2000 only and then restart it, when it is back on line the same error appears again.
Wondering and trying, I found that if at this point I run the same SP from the SSMS connected to Server2008, it does work and from this moment on the logic tier service also works again, without any modification on the link definition.
What am I missing? Isn't it really weird?
I hope my description is enough clear, and I'll very much appreciate your explanation and guidance to overcome this very bothering problem.
Thank you in advance