Jim's answer below is probably correct. I can't imagine why they would want a title search 1/2 way into rehab. It makes sense that the lender wants to be certain to assure all work completed has been paid for. They want to see that the construction money is being managed properly.
It makes no sense that they want to re-run title because any mechanics liens and claims from recent contractors wouldn't show up until it was litigated. I don't think any claims would show up that quickly. However, a Lis Pendis can be filed to stop any transfer of title while the litigation is pending. Maybe they want to see there are no Lis Pendis filed? I would ask the lender the reasoning behind this before agreeing to pay for another title search. Basically, if your deal is a good deal, the extra $100-200 for an additional title search shouldn't be a deal breaker.
Hope that helps. Good luck with your renovations.
All the best,
REALTOR, Property Manager
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Further, if a transaction is particularly "painful"; I promise ANY mortgage consultant would be trying every step possible to close it ASAP....both because we are paid upon completion of the transaction and because human nature ensures we all want headaches to go away, not stick and stay!!! Best to you, hope it all came together!