How is traditional thermite powder stored such that it doesn’t corrode?
Thermite powder is a heterogeneous mix and consists of fuel and oxidant, in you case aluminium $\ce{Al}$ and rust $\ce{Fe3O4}$. Separately, those can be corroded over time all right: aluminium can be oxidized and form aluminium(III) oxide, hydroxides and even some salts depending on what atmosphere thermite has been kept in. As you probably know, aluminium, being a reactive metal, doesn't corrode under ambient conditions as it's surface is protected by the thin layer of $\ce{Al2O3}$. Iron(II) is also capable of further oxidation, although rust is already the most stable form under ambient conditions.

However, it seems like you are using the term "to corrode" quite liberally to denote the act of burning of the thermite, e.g. the primary exothermic reaction

$$\ce{8 Al + 3 Fe3O4 → 4 Al2O3 + 9 Fe}$$

which only occurs when enough external energy (say, in a form of heat) is supplied. The thing is, not every reaction that is permitted by thermodynamics is also permitted by kinetics. Burning of a thermite is a heterogeneous process requiring to overcome activation barrier. Simply put, there are numerous solid particles or two phases being barely in contact, plus there is a protective layer on one phase ($\ce{Al2O3}$). Here, you need energy at least to increase thermal motion (promoting mass transfer between the phases) and compact the mix (ideally, melt to increase contact area).

That's why thermite won't easily go off, and it's a good thing making its storage safe and the working process predictable. There are only a few documented accidents [1, p. 62] resulting in ignition of thermite-alike mixtures, but none of them were spontaneous; instead, they were caused by the supply of substantial amount of external energy (heat, electricity, sparks, kinetic energy etc.), or third-party chemicals acting like catalysts:


  Aluminium-painted rusty surfaces are only hazardous if the coating has 
  been heated to 150 °C: on cooling, the hazard remains (Eckart et al., 1971). 
  Paints with cellulose nitrate as an additive are always hazardous. [...]
  
  Hawkins Colliery, 1950. The impact of a hand-held drilling machine cased 
  in Elektron C alloy (94% Mg) upon rusty steel scaffolding ignited 
  firedamp, burning 10 men, one fatally. This incident led to the initiation 
  of a major research programme into the dangers of light alloys by the 
  Safety in Mines Research Establishment. [...]
  
  SS Esso Durham, 1961. An explosion in one of the ship's tanks on 29th January was attributed to the impact of a brass object, of weight 361 b, onto a magnesium anode on the wall of the tank after a fall of 16 ft. From simulations of possible alternatives, it was considered likely that a grazing impact on the rough, dirty magnesium surface would have smeared the brass, which would then have reimpacted the anode a fraction of a second later, causing a thermite reaction and an explosion. The oxide necessary was probably provided by dirt in the area (ignitions were not obtained when impacting a clean magnesium surface). The possibility of ignition from impact onto hardened steel after a 40 ft fall was eliminated. [...]
  
  An aluminium anodizing works, Bletchley, Buckinghamshire, 1971. A ferrous metal object caused a spark on an aluminium grinding and polishing machine; the abrasive belts were lubricated by mineral oil, which caught light. The fire spread to the oil tank and extract ducting, causing £65000 worth of damage. [...]
  
  Horden Colliery, 1955. A steel weight was dropped on a friction prop with 
  aluminium frictional surfaces, leading to ignition of firedamp. 
  
  Glyncorrwg Colliery, 1955. A rusty steel wedge was struck from an aluminium roof bar, leading to ignition. 
  
  United Kingdom, 1971. Propane was vented into a workshop during the filling of 140 lb propane cylinders when one was accidentally overfilled. The propane was ignited, and two people were injured in the subsequent explosion. The ignition source was believed to have been a spark from rusty steel cylinders being loaded outside, which, on examination, were 
  shown to have aluminium smears on them. An aluminium roller conveyor was being used in the loading operation. A very light impact on such a smear is capable of generating a spark through a thermite reaction. [...]
  
  Ruhr Refinery, 1976. Two explosions within two hours of each other occurred on the 2nd December whilst switch-loading diesel into two tankers of carbon steel fabrication using an aluminium loading arm. The explosions were attributed either to a static electricity discharge or to a thermite reaction. [...]
  
  SS British Industry, 1963. The tanker had cathodic protection by incorporating a series of magnesium anodes in seven tanks. The cause of an explosion on the tanker was attributed to the impact of loose anode materials onto rusty deposits in the tank in which the explosion occurred. On examination after the explosion, many of the anodes were seen to be almost detached from their angle-iron bases, and bits had broken away. It 
  was deemed that detachment could have been effected by a washing machine whipping violently in the tank, and that there would have been flammable concentrations of crude oil vapour in the tank. 


References


Bond, J. Sources of Ignition: Flammability Characteristics of Chemicals and Products; Butterworth-Heinemann: Oxford; Boston, 1991. ISBN 978-0-7506-1180-0.