We define stealth Man-in-the-Middle adversaries, and analyse their ability to launch denial and degradation of service (DoS) attacks on secure channels. We show realistic attacks, disrupting TCP communication over secure VPNs using IPsec. We present: First amplifying DoS attack on IPsec, when deployed without anti-replay window. First amplifying attack on IPsec, when deployed with a `small' anti-replay window, and analysis of `sufficient' window size. First amplifying attack on IPsec, when deployed with `sufficient' window size. This attack (as the previous) is realistic: attacker needs only to duplicate and speed-up few packets. We also suggest a solution designed to prevent the presented attacks, and to provide secure channel immune to degradation and other DoS attacks. Our solution involves changes (only) to the two gateway machines running IPsec. In addition to their practical importance, our results also raise the challenge of formally defining secure channels immune to DoS and degradation attacks, and providing provably-secure implementations.