Ive never experienced this…
I’d say the Rample is designed to output modular levels signals…( * ) , you’d need to talk to Squarp , on why this might not be suitable for a headphone amp via the contact form.
(impedence related?)
if its only doing it with your headphone amp… and not (for example) if you plug the Rample into another Eurorack module… then frankly, Id say its not designed for that use-case. (**) … again, Squarp can given you details on this.
sorry, its speculation, but in this case… its always best to ask Squarp directly, as they are the only ones with the spec sheet for components etc, and theres not enough published on the website, to definitely answer this… so only the can give the true answer.
note: if Rample is restarting, its likely to be its ‘under-volting’ for some reason… basically too much power draw… (which given your supply, I would be concerned about)
btw: I dont think this would damage the Rample, but frankly, until you find out the cause… I would definitely not risk doing it again… in case its burns something out!
(*) bizarrely, I though Rample had an option for line level on the sum output (not the individuals) , but I cannot find a reference to this on specs/manual… either im blind, or just mis-remembered 
(**) generally you are ‘suppose’ to use output modules in eurorack, unless the module explicitly supports line level. similarly… Eurorack modules outputs are not designed to be used with headphone… unless of course they have a headphone jack 
in practice, many eurorack modules directly into audio interfaces and (external) mixers , and usually dont have issues… as these very often support modular levels (ymmv !)