Zend\Json\Server\Server::addFunction instantiates a new object even if an object is given as a callable.
e.g.
$server->addFunction(array($this, 'remoteProcedure'));

This gets problematic in case the constructor has arguments or the object needs further initialisation.
In contrast to this Zend\Json\Server\Server::setClass reuses the given object.

The behaviour is caused by the difference in the call to
Zend\Server\AbstractServer::_buildSignature

setClass:
$definition = $this->_buildSignature($method, $class); (line 133)

addFunction:
$definition = $this->_buildSignature($method); (line 109)

If there are no reasons against it the fix would be
using
$definition = $this->_buildSignature($method, $class);
as well in addFunction.