nurse a drink
Consume a drink slowly, especially in order to conserve it. For example, He nursed one drink for the whole evening. This idiom alludes to holding a glass very carefully, as one might a child. [c. 1940]
The American Heritage® Idioms Dictionary Copyright © 2002, 2001, 1995 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company.