Are air rifle scopes actually special?

Yes, air rifle scopes are different from firearms scopes in several ways. The two main differences are, airgun scopes are designed to withstand the recoil of a spring piston air rifle and they are parallax adjusted or adjustable for use at airgun ranges..

>>What are the chances of breaking it?<<
If you put a scope on a spring piston air rifle that is not designed to be used on one, you're just wasting money.

Airgun scopes
http://www.beeman.com/scopes.htm
http://www.airgundepot.com/air-rifle-scopes-overview.html
http://www.pyramydair.com/site/articles/ao-meaning

These sites explain the difference and why you should never put a firearms scope on a spring piston airgun..

>>I want to put a cheapo $40 scope on my break barrel<<
Leapers 3-9x40 Mil Dot($47)
http://www.pyramydair.com/cgi-bin/accessory.pl?accessory_id=2197

I'm sure you can find a much better deal than this if you do a little research. You might even be able to find what you're looking for at Wal-Mart since they carry CenterPoint and BSA airgun scopes.

Airgun/accessory sales
http://www.pyramydair.com
http://www.airgundepot.com
http://www.airgunsbbguns.com
http://www.airgunwarehouseinc.com

Non existent recoil? My RWS 34 kicks as hard as my brother-in-law's .22 WMR bolt action, just forward, not backwards.

On a 'springer gun' the 'recoil' is in the wrong direction.
It's not the magnitude, but the direction.
Also a standard scope will be parallax set at 100Yd.s ,
9further than you will be shooting.
There are 'cheapo' airgun scopes available in your price range.
Get the proper scope, You'll be happier with it.
Check out 'BSA scopes at midwayusa.com. for example.

Actually, the reverse recoil of the piston type of air rifle will damage a regular scope. They are designed to absorb the normal recoil of a cartridge gun. When exposed to a constant diet of reverse recoil, damage will occur. You must use a scope that is designed for the reverse recoil of an air rifle.

http://www.cl-sports.hk/

The first six over heat but it's not a problem with the heat It's more a problem of build up. The M240 Bravo shoots more than 800 rounds per minute and the barrel turns a glowing orange and has to be cooled and changed before it melts. Same for M249 SAW(squad automatic weapon) Same for the M2Hb The M134 I am not sure about. All these will still be accurate but as the operator you are trained to distinguish what is the malfunction of the individually assigned weapon.

The chances of breaking your scope... Pretty good actually, at least over the long run. Most firearms rifle scopes are designed to deal with uni-directional recoil. The bi-directional recoil of a spring piston airgun (especially the magnum spring piston airguns) is actually more damaging to a rifle scope than being mounted on an elephant gun (.416 Rigby, .458 Winchester Magnum, or .500 Nitro Express). In the short run a scope can probably take it, but over time the bi-directional recoil will probably scramble the inner workings of your scope if its not designed for use on spring piston guns.

Edit:
C_F_45 gave you a really great answer.

None.

Air rifle scope are the weakest ones made in the industry. The only reason you see them labeled as 'Air Rifle' scopes is to prevent someone from putting them a real gun.

Hope this helps