Patchelf'ed binary ignores long rpath

I am trying to patchelf a binary with many dependencies. I tried to add them one by one and at some point the binary started ignoring all the additional rpaths I was adding. For instance (I started adding the libraries to the nix profile to try to work around the issue):

$ patchelf --print-interpreter myapp

$ patchelf --print-rpath myapp

$ ./myapp
./myapp: error while loading shared libraries: cannot open shared object file: No such file or directory

$ ls /nix/var/nix/profiles/default/lib/   

But adding the path to LD_LIBRARY_PATH works:

$ env LD_LIBRARY_PATH=/nix/var/nix/profiles/default/lib ./myapp

Are there any constraints on how many paths can be added to the rpath?