No. Contracts are commonly awarded for a fixed term, and while an agency that is happy with the incumbent can renew or sole-source the next cycle without re-announcing, it cannot keep doing that indefinitely. Rules limiting consecutive cycles exist to prevent overly cozy relationships with contracting officers, so contracts eventually return to open competition.
For larger projects, the recompete must be publicly announced and attract multiple bidders, and may be re-announced if too few respond.
This rotation is good news for new contractors: contracts regularly come back onto the market, creating openings for registered vendors who are ready. The program's system flags previously awarded contracts approaching their recompete window, so members can introduce themselves to the agency and build familiarity before the opportunity officially drops — exactly when incumbents are most vulnerable.