Yes, MindMyMinistry keeps all your past services and you can refer back to them at any time.
To see your past events, just select the current (or previous) year from the "Show" box at the top of your Events page:
This will list all events, past or future, for 2015. You can then click on the title for any one of them to see the details.
Pro tip: If you want to find out how often songs are being used, you can go to the Songs page and look at the "No. of Plays" columns. These columns show you the number of times each of your songs have been used in the last 8 weeks and 12 months.