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We investigate the stability of a new class of BPS cosmic strings in N=1 supergravity with D-terms recently proposed by Blanco-Pillado, Dvali and Redi. These have been conjectured to be the low energy manifestation of D-strings that might form from tachyon condensation after D- anti-D-brane annihilation in type IIB superstring theory. There are three one-parameter families of cylindrically symmetric one-vortex solutions to the BPS equations (tachyonic, axionic and hybrid). We find evidence that the zero mode in the axionic case, or s-strings, can be excited. Its evolution leads to the decompactification of four-dimensional spacetime at late times, with a rate that decreases with decreasing brane tension., Comment: 6 pages, 5 figures