Scenarios that invoke multiple episodes of star formation within young globular clusters (GCs) to explain the observed chemical and photometric anomalies in GCs require that clusters can retain the stellar ejecta of the stars within them and accrete large amounts of gas from their surroundings. Hence, it should be possible to find young massive clusters in the local Universe that contain significant amounts (>10 per cent) of the cluster mass of gas and/or dust within them. Recent theoretical studies have suggested that clusters in the Large Magellanic Cloud (LMC) with masses in excess of 10... M... and ages between 30 and ...300 Myr should contain such gas reservoirs. We have searched for H...I gas within 12 LMC (and 1 Small Magellanic Cloud) clusters and also for dust using Spitzer 70 and 160 μm images. No clusters were found to contain gas and/or dust. While two of the clusters have H...I at the same (projected) position and velocity, the gas does not appear to be centred on the clusters, but rather part of nearby clouds or filaments, suggesting that the gas and cluster are not directly related. This lack of gas (<1 per cent of the stellar mass) is in strong tension with model predictions, and may be due to higher stellar feedback than has been previously assumed or due to the assumptions used in the previous calculations. (ProQuest: ... denotes formulae/symbols omitted.)