Are molecules with bond orders less than one stable?
Molecules possessing a bond of order below 1 can be perfectly stable, in the sense that their resulting molecular structure lies in an energetic potential well. Strictly speaking it is enough that at $T=\pu{0 K}$ and in the absence of any interactions with matter or fields, the molecule will not spontaneously disassemble. However, there is no need to go quite so far to protect such a molecule from decomposing; there are examples of species which are chemically important in regular laboratory conditions.

All other things being equal, it is true that species with bond orders below 1 are relatively unstable. This is mainly because the fractional bond is comparatively weak (requiring comparatively little activation energy to break, i.e. a smaller $E_\mathrm{a}$), and because in most cases the molecule can react with other substances in such a way as to form products with all covalent bonds of bond order 1 or higher (increasing the exergonicity of most reactions, i.e. a more negative $\Delta_\mathrm{r}G$). 

Since the kinetic barrier for reaction is comparatively low, and the thermodynamic drive for reaction is comparatively high, species with bond order below 1 tend to need some extra protection against the world to stay in one piece. For example, diborane and trimethylaluminium are compounds possessing bonds of order 0.5, and while being indefinitely stable when pure, they spontaneously ignite in air from exposure to oxygen and moisture. As rightly pointed out in the comments, noble gas compounds require fractional bond orders, yet several compounds can be obtained and stored (especially xenon compounds), though they tend to be sensitive to moisture and heating. Boron is also responsible for a very interesting class of compounds in which many boron atoms attach to  each other in cage-like structures with very complicated bonding, in which fractional order bonds are involved. Some of the larger and more symmetric structures can be relatively stable, especially with adequate substituents. 

In space, there's really not much of anything around, so you might expect to find some molecules with fractional bond orders floating about. Indeed, one can find the trihydrogen cation, which is actually one of the most common ions in the Universe!