Reports - Problem 503 Message
503 is a generic error, but usually means a report has timed out loading or the system is predicting it will time out.
A common cause is a report that was saved with View All selected, making the report display all the rows on one page.
This example in edit mode loads and displays 2,352 rows of data:

But if someone changes the filters such that tens or hundreds of thousands of rows need to be displayed on one page, that may not end well.
The slowest part of any report is building and displaying the data table. Saving such a report with "View 20" should let it run with hundreds of thousands or rows. Even if you are only displaying the first 20 rows of a report, column breakdown counts, crosstabs, and summations give you counts for all the data, not just the rows that are displayed.
If you need to see tens or hundreds of thousands of rows of data, export to CSV is the fastest option.