Isolate recurrent pattern vs. evolving background sound
So, assuming the linear superposition you suggest, the sound you want to exctract lives in a periodic subspace of your signal space. This subspace is uniquely characterised by the exact spacing between the sound instances, which I assume you know in the following. If you don't know it, you can find it from calculating the autocorrelation sequence of your composed signal.

Without further knowledge, the only linear method for finding your sample is to project the composed signal onto the periodic subspace it lives in. There are two obvious ways you can do this. 

The first is taking the Fourier series of the composed signal and nulling all coefficients that do not belong to an integer multiple of the frequency corresponding to the period length of the repetition. Summing the modified series will give you the desired signal. 

The second is to just accurately cut the sample into segments that align perfectly with respect to the repetition period and just sum all those segments up into a single sample.

The result of these two operations will give you a representation of the composed signal the same periodic subspace. However, since the subspace is relatively large compared to the total signal, there will be components of the composed signal that are contained in this subspace by mere chance. So the separation will be far from perfect. You can improve the separation by taking more repetitions, make the full signal space much larger than the periodic subspace.

If you need a better method you won't get around characterising the nature of the signal you want to extract. That's where perception models, source models, statistical signal models, etc come in. I cannot really go into this in this answer. It's a topic that fills many books and is in general very difficult.