the poly A tail is bound by the poly-A binding protein (PABP, or Pab1 in yeast). PABP associates with the eIF4F complex that is bound to the cap. eIF4F is at competition with the DCP1/2 decapping complex.
the poly-A tail is shortened (presumably during translation) by the CCR4-NOT and PARN complexes. as the poly-A shortens, there are less PABP that can associate with the eIF4F. Once the poly-A is short enough, the eIF4F-cap complex is less stable, leading to successful recruitment of the decapping complex to the cap. decapping is considered the "point of no return" since exonucleolitic degradation by Xrn1 is fast.
(the above is obviously a simplified description - the poly-A and PABP are central players that interact with multiple partners - both translation & degradation proteins - that can affect the stability of the mRNA).
It should be noted that poly-A tail that is added to other types of RNAs actually leads to de-stabilization of the RNA.