We consider a set of primary channels that operate in an unslotted fashion, switching activity at random times. A secondary user senses the primary channels searching for transmission opportunities. If a channel is sensed to be free, the secondary terminal transmits, and if sensed to be busy, the secondary transmitter remains silent.We solve the problem of determining the optimal time after which a primary channel needs to be sensed again depending on the sensing outcome. The objective is to find the inter-sensing times such that the mean secondary throughput is maximized while imposing a constraint over the maximum tolerable interference inflicted on the primary network. Our numerical results show that by optimizing the sensing-dependent inter-sensing times, our proposed scheme reduces the impact of sensing errors caused by false alarm and misdetection and outperforms the case of a single sensing period.