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Are you distributing those press releases to others sites (via RSS)? In other words, do they appear on outside sites in their identical form? If so, you could use rel-canonical cross-domain or a syndication-source tag and point your copies to the original press releases. That should help offset any duplicate content issues. It will keep you from ranking directly for those press releases, though. It really depends on the goals/scope. It's not uncommon to cross-post press releases, and if you're talking about one a month or so on a site with dozens of pages (or more), it's not a big issue. If you're talking about 100s of press releases, then you could certainly run into trouble.

If you use 301 redirects you shouldn't lose any results.