Another way of looking at it is that basically all iron on Earth is found in the form of iron oxide, so iron compounds do not tend to stay oxidized over large time scales. Similarly, aluminum reacts with oxygen rapidly and is hardly ever (but not never) found in nature as an elemental metal. Some surface treatments such as anodization can extend this time, but will eventually fail. Some elemental metals can be found in nature, which is an indication that under some conditions they could be found as fossils. These "native metals" particularly include copper, gold, silver and platinum-group metals (see link for a full list).

If, however, a reactive metal object is kept well away from oxygen and water it may last much longer. This is the case for satellites, although most satellites orbits are not entirely stable. The longest lasting may be those boosted into graveyard orbits; standard geosynchronous satellite graveyard orbit results in an expected orbital lifetime of millions of years. Objects on Mars stand a good chance of lasting for long time scales, since they are not exposed to air or water, and are kept cold with little thermal cycling. They are also likely to become buried in dust blown by the Martian wind. The Philae comet lander may be similarly preserved, though comets tend to crash into planets after a few million years. Similarly, several of the outer planet probes may last for extreme time scales since they will be in vacuum, cold, and safe from major collisions. In particular: Voyager 1 & 2, Pioneer 10 & 11, New Horizons. But these are continuously moving away from the solar system, so while preserved, won't leave any fossils to find.

In total, the answer appears to be eons, but few objects will find suitable conditions, and the best place to look will be on Mars.