Existing proof-of-work cryptocurrencies cannot tolerate attackers controlling more than 50 percent of the network's computing power at any time, but assume that such a condition happening is unlikely. However, recent attack sophistication, e.g., where attackers can rent mining capacity to obtain a majority of computing power temporarily, render this assumption unrealistic. This paper proposes RepuCoin, the first system to provide guarantees even when more than 50 percent of the system's computing power is temporarily dominated by an attacker. RepuCoin physically limits the rate of voting power growth of the entire system. In particular, RepuCoin defines a miner's power by its 'reputation', as a function of its work integrated over the time of the entire blockchain, rather than through instantaneous computing power, which can be obtained relatively quickly and/or temporarily. As an example, after a single year of operation, RepuCoin can tolerate attacks compromising 51 percent of the network's computing resources, even if such power stays maliciously seized for almost a whole year. Moreover, RepuCoin provides better resilience to known attacks, compared to existing proof-of-work systems, while achieving a high throughput of 10000 transactions per second (TPS).