I have recently come across an issue, where Azure users are trying to remotely connect to one of the role instances and getting stardard time out error message similar to below.
"The remote connection has timed out. Please try connecting to the remote computer again"
RDP(Remote desktop) connection to other role instnaces might work as expected. Issue is with only one or few role instances
There are few known issues that prevent remote desktop connections to instances in the following scenarios:
Issue occurs due to stale data maintained by Remote forwarder service.
The issue can be resolved by rebooting all instances of the role that imports "RemoteForwarder" Module. You can identify the role that has "Remote Forwarder" module using ServiceDefinition.csdef file. Role under which you see the below configuration elelement is the one you should reboot.
<Import moduleName="RemoteForwarder" />
Rebooting of the role instances can be done from Portal itself.
Hope this Helps!