There can legitimately be a lot of hold ups in this - but the timescales you are quoting do seem a little extreme.
It may not be simply the case of "getting your name off the mortgage"; and may be similar to repaying it and having an entirely new one drawn up in his /his and her name. If this is the case then everything which could hold up a mortgage can be happening (i.e. issues with deeds, searches, valuations etc.) particularly if its with a new lender.
Something which may be adding to the timescales if the new person moving in is not going to be on the mortgage. In which case lenders have to go through several extra hoops to ensure that she is fully aware
of what he is doing if she will be in some way financially contributing to the upkeep of the home. Google RBS vs Etridge if you care for the boring legal details.
Indeed, the above point also is applicable if there is anyone else over 18 in the house, or if the mortgage is being used to secure any business liabilities.
But. your solicitors should be able to tell you all of this.
Unfortunately, like many things these days, if you want something done you have to make a fuss. Its boring and painful, but I would start harassing your solicitor at least weekly. Even if its not their fault, they will get sick of speaking to you and start harassing his solicitors. If its not their fault they'll harass him.