Maybe best to stick a thicker grease then, however you want something that won't dry out quickly.

I'd give a good oil supplier a call and see what they recommend.
Lots of the more common greases (including CV/Moly grease) will dry out surprisingly quick when open to the atmosphere and a bit warmth. The only grease I've used lately that never seems to dry out, is a red grease from the local agricultural dealers, but it may be a bit on the thick side.