Hi

If you're URL / permalink is not changing than in theory all the off-page SEO for the page will be unaffected since the page still exists. So external link juice still has some where to go (to coin a phrase). But beware of the anchor text of the link (well be aware) - more about this below:

Andy makes a good point in that if you are changing manufacturer than most likely some of the text will change ( obviously "Nike" changes to "Gap" for example). So from an on-page SEO perspective the page has changed and this might affect how well the particular page ranks for "Nike Green Sweater" since quite obviously that particular page is no longer about Nike Green Sweaters and assuming the search engine bot is doing its job it will work this out and adjust indexing for that brand specific keyword combination.

To deal with that potential problem, I would suggest adding a link to the Nike Green Sweater page on the Gap Green Sweater page - you can do this quite naturally by adding a "related products" link or "people who bought this also bought" or "looking for Nike Green Sweater?" (for example).

This passes some of the link juice for your page to the Nike Green Sweater page.

Helping Nike Green Sweater Wearers...or Another Reason for an Internal Link:

Creating an internal link to the Nike Green Sweater page also helps people who came to your site through a link that explicitly referred to "Nike Green Sweaters" and were looking for "Nike Green Sweaters". (You could use a tool like AHREFs or Google Webmaster or Open Site Explorer to find the anchor text being used by people externally linking to you to get a sense of the scale of this "problem". )