Okay, done some more testing, and I simplified the case too much here. The test I provided works, but the full case does not (works in 5.6.0). I will have to reinvestigate.

It has nothing to do with the eval, and has to do with $this not being available from an included script.

Create second file called hello.php:
####
<php?

echo $this->hello;
####

Use this test case from another file:
####
class Test
{
	public $hello = 'hi';

	public function testNow()
	{
		require('hello.php');
	}
}

$o = new Test();
$o->testNow();
####

updated title

I can't reproduce this (with neither eval nor require).

Okay, yes hello.php does output 'hi' as expected, but the content is changed to
###
var_dump($this);
###
It outputs NULL, which is not expected, especially since var_dump($this->hello) results in string(2) "hi".

Now, to get hello.php to stop outputting 'hi' altogether, my hello.php is more complicated (and closer to the format of the real code that isn't working):
####
if (!function_exists('test_fn'))
{
	function test_fn(&$obj)
	{
		echo $obj->hello;
	}

	class NestedTest
	{
		public function doubleTest($obj)
		{
			echo $obj->hello;
		}
	}
}

test_fn($this); // outputs nothing, expected 'hi'

$o2 = new NestedTest();
$o2->doubleTest($this); // also outputs nothing, expected 'hi'
####

Fixed in https://github.com/php/php-src/commit/58f389772f19ef604ad151407c7f878fadea6c5f, thanks for the report :)