Put new screws in the top and tighten down any old screws.  If you put them together with nails, use screws.

Something else you may want to try;  Take the top off the platform and cover all top supports with sheet foam (noise damping) or even fabric or old newspapers (TWO layers - as they did in the 30's) and put the top back on with screws (as has been suggested).   The squeaks come from wood rubbing against wood with very LITTLE movement.  If you buffer the two wood surfaces, no more squeaks!

With wooden frame rostra, all of the suggestions posted by everyone are good quick fixs, try the lot.
But what your probably experiencing is whats called 'lateral frequency vibrations' on a small scale, at the moment.
Look at the structure of the rostra frame & it's  jionts, how are they put together?
As they are used quite a bit the rosra is suffering from fatigue & starting to losen up from being constantly performed on.
Any movement from being walked on will generate a lateral frequency causing these squeekers.
This is normaly not a problem with unit rostra, if they have good jionts & diagonal bracing.
All the reasons given are probably happening to them & becoming more pronounced as time goes by.
they are probably 2.4m (8') x 1.2m (4') units which are normal & stable enough, depending on hieght.
But as the squeek is becoming more of a problem, this may be a warning  or  just as the previous posters have suggested, an easy remedy problem.
If you have a Chipy on hand who can give them the once over to ensure there is not a major problem lurking with the structure & how they are put together.
I'm not trying to alarm as it may be just lack of general maintence & a fiew ruddy jionts are the problem. But it would be a compfort to asses the risk that is not a safety issue.
It is quite surprising how much & quickly lateral frequency vibrations can build  as you add the  warm prop factor.

 
 

Desqueeking is normally as simple as you Dana & Patrick have suggested, thru rescrewing & general maintenance.
Especialy when the ply starts to delaminate  with yawns & smiles appearing along the edges of the ply.
That's a good idea just to flip over the plates & rebedding, with new new tek screws for a fresh top is worth the effort.
If you get your hands on some marine ply, the type they use on building sites, for concrete form work. It is expensive to buy off the shelf, but it can be obtained cheaply via salvage & industrail waste recyle yards.
There again if you know a friendly builder or a new building site. A few comps can procure a heap of gear, besides skip diving before the boards are normally broken up to chuck out.
In other cases wood on wood rubbing, as mentioned by spectrum is a source for the squeekers to exist. which for the most part can be dampened by the method posted & also mentioned by the others.
 In a lot of venues where nails seam to be the diet of mechs, techs & helpers. I try to  get them to  change thier feeding habits & relish the delights of tek scewing. Whereby posi drives & the tek gun becomes thier very bestest play thing. untencil & toy.
Nails have thier place in the other world, but only spariingly in the reality of back stage. It can be very difficult to ween them off & an ardious task, if withdrawl kicks  in - well worth the effort though in my opinion!
Nailed jionts, as Patrick pionted out are a pime suspect, with constant flexing & cavorting of unglued jionts.
Flapping, drumming & bumping. Are easy visual & audable things to fix with the excelent methods suggested by Martw, Nanette & Spectrum. But squeekies can drive you round the twist tracing them. They breed like rabbits & mysteriously as wire coat hangers populate in a wardobe or closet.
But even with a stock of rostra 75director they will return as fast as a crook smell.



  

If you choose to fix with nails consider using ring nails or the type that have a lacquer that makes them stay in better or longer. (Joe or Patrick probably know what they are called, I've forgotten) Either will stay put longer.

I was a little surprised that you heard 'squeak' and not the echoing footsteps that plague large patforms.  Has anyone done sound dampening to these already?