Ultra-light axions have sparked attention because their tiny mass m∼10^−22 eV, which leads to a Kiloparsec-scale de Broglie wavelength comparable to the size of dwarf galaxy, could alleviate the so-called small-scale crisis of massive cold dark matter (CDM) candidates.However, recent analyses of the Lyman-α forest power spectrum set a tight lower bound on their mass of m≳10^−21 eV which makes them much less relevant from an astrophysical point of view. An important caveat to these numerical studies is that they do not take into account attractive self-interactions among ultra-light axions, which can counteract the quantum "pressure" induced by the strong delocalization of the particles. In this work, we show that even a tiny attractive interaction among ultra-light axions can have a significant impact on the stability of cosmic structures at low redshift. After a brief review of known results about solitons in the absence of gravity, we discuss the stability of filamentary and pancake-like solutions when quantum pressure, attractive interactions and gravity are present. The analysis based on one degree of freedom, namely the breathing mode, reveals that pancakes are stable, while filaments are unstable if the mass per unit length is larger than a critical value. However, we show that pancakes are unstable against transverse perturbations. We expect this to be true for halos and filaments as well. Finally, we also assess whether these instabilities can leave a detectable signature in the Lyman-α forest. We find that unstable filaments could be seen as absorption lines with column densities of neutral hydrogen NHI≲10^17 cm^−2 even for an axion decay constant as large as f≲10^16 GeV. We hope our work motivates future numerical studies of the impact of axion self-interactions on cosmic structure formation.