It's rare and is usually because the engineer is worried about the ability of the designer or builder to properly carry out the design or you are only paying him a small fee. Liability insurance is expensive. Are you asking him to review the work during construction?

I don't know why the contractor would have an issue with it; the engineer is working for you.

I wouldn't sign it, and wasn't asked to sign anything like that when we hired an engineer.

If you are doing a large remodel you should have an attorney review the contracts, and he or she could help you with this.

I had a project that took some time to find a structural engineer willing to put his stamp on his design making him liable for defects. But I haven't found one who insisted on limiting his liability the way op's proposes. So say I pay the PE a typical $1,000 to review the building plans; he leaves out some important supports and half the second floor sags a foot once the drywall is on. Do you think $3,000 would cover the repairs?

On the other hand, if the OP only gave the engineer a hundred bucks to size a steel beam he might not think the fee justified taking responsibility for the project.

We don't really know the scope of work or the terms of the agreement.

If he is doing the structural design then he should be on the hook for at least up to the limit of his professional liability insurance "otherwise known as E&O (errors and omissions) insurance>. This limit is typically $2 million but sometimes $1 Million. The cost of E&O insurance can be sizable, but that is already factored into his price and if he gets you to limit his liability, then you are not getting something that you in effect are already paying for. The contractor is taking issue with it because if there is a structural failure, even if it's because of a faulty design, the contractor will be brought into any lawsuit and have to pay to defend it even if he is not ultimately found to be liable - he wouldn't have any viable place to seek reimbursement if the engineer's liability is limited.

Well, there's the rub. We don't know what "structural design" means in this instance because the OP didn't describe the scope of the engineer's services. Since the structural elements of a single family house are normally described in great detail in the applicable building code, the structural engineer's services might consist of designing a complicated vertical and horizontal load transfer system in an earthquake or high wind zone or those services might consist of sizing a single LVL or steel beam.

So many of the questions on the GardenWeb should be answered with "it depends on what you are talking about" rather than a long discussion based on a wide range of assumptions. If OP's want useful answers they need to describe the situations better IMHO.

Start with the scope of structural work and the nature of the various contracts and then describe the engineer's fee and liability insurance as well as that of the Designer.