The last decade consolidated the cyberspace as fifth domain of military operations, which extends its preliminarily intelligence and information exchange purposes towards enabling complex offensive and defensive operations supported/supportively of parallel kinetic domain actuations. Although there is a plethora of well documented cases on strategic and operational interventions of cyber commands, the cyber tactical military edge is still a challenge, where cyber fires barely integrate to the traditional joint targeting cycle due to, among others, long planning/development times, asymmetric effects, strict target reachability requirements, or the fast propagation of collateral damage; the latter rapidly deriving on hybrid impacts (political, economic, social, etc.) and evidencing significant socio-technical gaps. In this context, it is expected that Tactical Clouds disruptively facilitate cyber operations at the edge while exposing the rest of the digital assets of the operation to them. On these grounds, the main purpose of the conducted research is to review and in depth analyze the risks and opportunities of jeopardizing the sustainability of the military Tactical Clouds at their cyber edge. Along with a 1) comprehensively formulation of the researched problematic, the study 2) formalizes the Tactical Denial of Sustainability (TDoS) concept; 3) introduces the phasing, potential attack surfaces, terrains and impact of TDoS attacks; 4) emphasizes the related human and socio-technical aspects; 5) analyzes the threats/opportunities inherent to their impact on the cloud energy efficiency; 6) reviews their implications at the military cyber thinking for tactical operations; 7) illustrates five extensive CONOPS that facilitate the understanding of the TDoS concept; and given the high novelty of the discussed topics, this paper 8) paves the way for further research and development actions.