I suspect you're only reporting the last error in a stack like this:
ORA-04068: existing state of packages has been discarded
ORA-04061: existing state of package body "schema.package" has been invalidated
ORA-04065: not executed, altered or dropped package body "schema.package"
ORA-06508: PL/SQL: could not find program unit being called: "schema.package"
If so, that's because your package is stateful:
The values of the variables, constants, and cursors that a package
declares (in either its specification or body) comprise its package
state. If a PL/SQL package declares at least one variable, constant,
or cursor, then the package is stateful; otherwise, it is stateless.
When you recompile the state is lost:
If the body of an instantiated, stateful package is recompiled (either
explicitly, with the "ALTER PACKAGE Statement", or implicitly), the
next invocation of a subprogram in the package causes Oracle Database
to discard the existing package state and raise the exception
ORA-04068.
After PL/SQL raises the exception, a reference to the package causes
Oracle Database to re-instantiate the package, which re-initializes
it...
You can't avoid this if your package has state. I think it's fairly rare to really need a package to be stateful though, so you should revisit anything you have declared in the package, but outside a function or procedure, to see if it's really needed at that level. Since you're on 10g though, that includes constants, not just variables and cursors.
But the last paragraph from the quoted documentation means that the next time you reference the package in the same session, you won't get the error and it will work as normal (until you recompile again).
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