When suspended particles are pushed by liquid flow through a constricted channel they might either pass the bottleneck without trouble or encounter a permanent clog that will stop them forever. But they might as well flow intermittently with great sensitivity to the neck-to-particle size ratio D/d. In this work, we experimentally explore the limits of the intermittent regime for a dense suspension through a single bottleneck as a function of this parameter. To this end, we make use of high time- and space-resolution experiments to obtain the distributions of arrest times between successive bursts, which display power-law tails with characteristic exponents. These exponents compare well with the ones found for as disparate situations as the evacuation of pedestrians from a room, the entry of a flock of sheep into a shed or the discharge of particles from a silo. Nevertheless, the intrinsic properties of our system seem to introduce a sharp transition from a clogged state (power-law exponent below two) to a continuous flow, where clogs do not develop at all. This contrasts with the results obtained in other systems where intermittent flow, with power-law exponents above two, were obtained.