max-mini-window-height

max-mini-window-height is a variable defined in `C source code'.
Its value is

0.25

Documentation:
Maximum height for resizing mini-windows (the minibuffer and the echo area).
If a float, it specifies a fraction of the mini-window frame's height.
If an integer, it specifies a number of lines.

You can customize this variable.

This variable was introduced, or its default value was changed, in version 23.1 of Emacs.