You can get a look into the process of transmitting a bundle of reports through the Transmission option under Administration|Report Settings.
A log file is created every time a particular bundle is distributed (usually via a scheduled task). This allows you to view a summary of the most recent 'transmission' of your reports.
The first screen lists all of the bundles that have log-files available. It also provides a breakdown of all of the different report subscriptions that are active.
Clicking on the name of the bundle allows you to see the transmission details.
The left/upper box contains the report timing - how long it took to generate each one of your reports.
Unusually long-running or short-running reports can indicate issues - it's often worth keeping an eye on any change in execution time if there wasn't an update to the report logic.
The right/lower box contains report distribution details - if sending the reports was successful.
When everything is working normally, all of the items in this list should be green. Any red items indicate a failure in producing or transmitting that report.
This failure may be due to service outages, problems with the address, security keys etc. Depending on the transmission method, this page should hopefully include some detail as to why the delivery failed.