There are some things that aren't available in protected worksheets.

Merging cells is in that group.

If you really, really want to (I wouldn't!), maybe you could provide a macro
that:
unprotects the sheet
merges the cells you want merged
reprotects the sheet

Protect Sheet but be able to merge cells wrote:

Does anyone know how to Merge cells once you have protected a sheet? There is
the option to 'allow users to format cells', but for some reason it will not
let me merge cells!!!

--

Dave Peterson