No se me caen los anillos

[poli]

Does this mean : I don't get embarrassed or I don't get discouraged? -- or
something else?

[Perikles]

My dictionary states familiar and ironic but avoids a translation, giving:

no se lo pidas a él que se le pueden caer los anillos
don't ask him to do it, that sort of thing is beneath him

no se te van a caer los anillos por hacer las camas
making the bed isn't going to kill you

[JPablo]

Well, here are the examples given in Oxford Superlex,

caérsele los anillos a alguien (familar & irónico): no se lo pidas a él que se le pueden caer los anillos = don’t ask him to do it, that sort of thing is beneath him o he won’t dirty his hands with that kind of thing; no se te van a caer los anillos por hacer las camas = making the beds isn’t going to kill you;

If I say, "no se me caen los anillos si tengo que ir a tirar la basura" I mean that taking the garbage out to the container is not going to kill me, it is not "beneath me". Like I remember a priest in a little village who used to work as a construction worker, building a small wall by the church... he would say, "A mí no se me caen los anillos por trabajar con los ladrillos..." That type of idea. I don't get embarrassed (as you mention) if I need to do a task considered to be a 'lowly" one. I take considering that a person with rings (anillos) is not used to do any 'heavy-duty' kind of work.
For example, "A mí no se me caen los anillos si tengo que limpiar el inodoro [WC], prefiero tener un lugar higiénico..."

I never heard this in the sense of "don't get discouraged", although one could say something encouraging (although a bit sarcastic/ironic), by saying to a kid starting to learn basketball, "¡Vamos, que no se te vayan a caer los anillos... pasa la pelota con más energía!" :)

Moliner gives,
Caérsele a alguien los anillos (informal). Frase con que se alude a algún trabajo o menester que una persona rehúsa o puede rehusar hacer por considerarlo humillante. Se usa generalmente en forma negativa: ‘A mí no se me caen los anillos por fregar el suelo’.

[poli]

Thanks guys. I think there are related English phrases. One that sounds a little New Yorkish to me is hoity toity; the other is high horse.
He's to hoity toity to go work in the garden. A él se le caería los anillos trabajar en un jardín.
He's on too high a horse to go out a drink beer at that tavern.

Do you think this anillos phrase is only used in Spain?

[JPablo]

Thanks, Poli, these "hoity-toity" and "high horse" expressions seem to match the idea. (Creo que van ¡"como anillo al dedo"!)

As far as other places besides Spain, I think it is understandable, but maybe less used than in Spain... Angélica, Chileno, Ookami and maybe others can confirm or deny that... (It is also in DRAE.) :)

[AngelicaDeAlquezar]

De acuerdo con los ejemplos de Perikles, la expresión se entendería por contexto, pero no se usa aquí.

[JPablo]

Curioso... en España es super-común. (A ver qué nos cuentan de otros parajes... Chile, Argentina...) :)