The dime was last changed in 1946 , to apear as it does today.
Previous to then it was the famous liberty dime. With the change of the Quarters and the paper money changes , perhaps the dime could use an upgrade. However I dont think Roosevelt should be removed for the likeness of Reagan.

Heres what I mean...

Some of the people and images that have graced the American coinage:

Abraham Lincoln ,Thomas Jefferson , Native Americans , Countless variations of Lady Liberty , Franklin Roosevelt , George Washington , The Actual 50 States , Benjamin Franklin , John Kennedy , The Bald Eagle , Dwight Eisenhower , Susan B. Anthony , and Sacagawea.

Perhaps its just me but I dont think Reagan belongs to that list.