Playing splitscreen Horde mode seems to bug Gears of War 3 out. Specifically, it seems to be limited to splitscreen Horde play with two profiles. When the bug comes in, it permanently breaks one of the profiles, not allowing it to enter any game mode anymore.
Epic Games is aware of it and replies: “Getting this resolved is a priority for Epic. We are collecting information internally, sourcing as much as possible from the community and exploring potential fixes. We do not have any recommendations to share with players just yet."
Expect a fix soon enough, but until then, stay away from splitscreen horde mode.