We demonstrate single-atom resolved imaging with a survival probability of $0.99932(8)$ and a fidelity of $0.99991(1)$, enabling us to perform repeated high-fidelity imaging of single atoms in tweezers for thousands of times. We further observe lifetimes under laser cooling of more than seven minutes, an order of magnitude longer than in previous tweezer studies. Experiments are performed with strontium atoms in $813.4~text{nm}$ tweezer arrays, which is at a magic wavelength for the clock transition. Tuning to this wavelength is enabled by off-magic Sisyphus cooling on the intercombination line, which lets us choose the tweezer wavelength almost arbitrarily. We find that a single not retro-reflected cooling beam in the radial direction is sufficient for mitigating recoil heating during imaging. Moreover, this cooling technique yields temperatures below $5~mu$K, as measured by release and recapture. Finally, we demonstrate clock-state resolved detection with average survival probability of $0.996(1)$ and average state detection fidelity of $0.981(1)$. Our work paves the way for atom-by-atom assembly of large defect-free arrays of alkaline-earth atoms, in which repeated interrogation of the clock transition is an imminent possibility.
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