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Suppose that we have a (combinatorial if necessary) model category $M$, and let $F:Delta^oprightarrow M$ a simplicial object in $M$, such that for any natural number $n$, $F([n])$ is a fibrant object in $M$.
We define a new object $X= colim_n F([n]) $. Is it true that $X$ is a fibrant object ?

No, it is not.

If what you mean by $rm colim_n$ is the actual colimit of $F$ as a diagram of shape $Delta$, then this colimit is isomorphic to the coequalizer of the two maps $F([1]) rightrightarrows F([0])$. Coequalizers rarely preserve fibrancy, and with a little thought we can think of a counterexample that extends to a simplicial object. Let $M$ be a model category in which coproducts of fibrant objects are fibrant (e.g. simplicial sets), and let $G:Dto M$ be any diagram of fibrant objects whose colimit is not fibrant (such as a cospan $X leftarrow Delta[0] to Y$ in simplicial sets for almost any Kan complexes $X$ and $Y$). Let $F$ be the simplicial bar construction of $G$, with $F([n]) = coprod_d_0 to cdots to d_n G(d_0)$. Then each $F([n])$ is fibrant by our assumptions on $M$ and $G$, but the colimit of $F$ is the coequalizer of $coprod_d_0to d_1 G(d_0) rightrightarrows coprod_d G(d)$, which is just the colimit of $G$ (it is the usual computation of colimits in terms of coproducts and coequalizers).

If instead what you mean by $rm colim_n$ is actually the geometric realization, then there is an even easier counterexample. Let $M$ be simplicial sets, let $X$ be a simplicial set that is not a Kan complex, and let $F([n]) = X_n$ regarded as a discrete simplicial set. Discrete simplicial sets are Kan complexes, so each $F([n])$ is fibrant, but the geometric realization of $F$ is just $X$ itself, which is not fibrant.