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As every customer is important and in Marketing process you put all leads in funnel and filter them and then keep rest in pipeline ,that means you cant ignore any customer because it can become a future prospect.
if its tough customer I think approach should be bit careful as you have mentioned customer doesnt convince easily and others had difficulty selling.
First step should be doing analysis on last sales call made if data available what were the reasons customer has not bought product , if reason was there was no NEED and salesperson kept pushing, If he/she forgot to add value with product or service offered.
Was customer concerned about after sales support, If customer has different mind set about the company which offered product during last sales call, so such factors surely will give a good idea why customer objected.
Take care of such issues and put your best step forward I am sure this SALE will be successfully trhough if not make such a rapport that they call you when there is real need for offered product /service.