Google is strict to link selling but no strict to affiliate links.You can still keep your affiliate links.

Once you get your Pagerank you can again continue writing sponsored posts.If Google make your PR 0 then reconsider again.

Thanks for the useful information. Can I still keep the affiliate links to sponsored review sites like PayPerPost? Or do I need to remove them too?

Yes I have been also penalized by Google before.But after reconsideration I got PR3.

I suggest you to remove the tracking image or small banners of the advertisers from your sponsored post.After that ask Google for reconsideration.Once you ask for reconsideration Google will reply you after few days or weeks.You can see the Google reply message in Webmaster’s dashboard.If they find that you were not violating their Webmaster’s Guidelines then they will give your Blog pagerank in next Update.

Have you been penalized before? For what reasons? How long did Google took to reinstate your blog PR?

I lost my PR (once it was PR4), mainly due to few sponsored posts. I have stopped writing for sponsors since. And would like to get back on G’s index.