At what point or stage should a marketing or sales personnel give up on a new customer?

never ever.

we need to understand his or her needs.our product might  not  be suitable for the market segment we are concentrating on.get their feedback,understand what they need and go back to product design and product engineering  and communicate clearly  your findings.

dono't give up, problems are opportunities,if you have  customers find out what they need and supply with excellence or somebody else will

When to give up is when you realize you logically can't please him. But as long as he knows how to understand reason giving up should be out of the question. It must be considered as a challenge. For you might probably learn a lot from this. Problem is one of the best opportunity to learn. Problem exist to makes us grow as individual and to make us better person in the future.

The efferts of Sales and Marketing personnel can generate the new customers for their products with the help of the following tools.like are 

1)  Keep attaintion to your customer in the right time

2)  sellect the right place for sale of your products

3)  with the help of  the social media 

4)  with help of the printing media

5)  through personal relationship

6)  and through sales promotion

You give up when the customer leave only .

Evaluate your time cost. If you feel that the amount time spent in converting a prospect to customer is exceeding the cost of the project, it is time to look for other customers. But do not completely bring down the shutter. A regular follow up should always be there, just to ensure your company is effectively positioned.

Once the customer stops responding to your repeated calls and mails. Otherwise there is no reason to shy away from you..

Give up? In my opinion NEVER.
I'd rather let the customer give up first.
I think while arguing with a socio-cultural view difference, that's where you learn a lot.
You can find ways to adapt.
But if you're not willing to do that and prefer to back up...this might result in a very bad personal situation.
Honestly I had a lot of these customers.
Some gave up and others turned out to be potential customers...

When there is no further room for price relaxation