Callable bonds may not be called immediately after a rate decrease because

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Callable bonds often have a call price that is at a premium above the par value of the bonds, which means that calling the bonds immediately after a rate decrease would require the issuer to pay more than the face value of the bonds. Additionally, the call provision is often deferred for several years after the bond's issue, which means that the issuer may not be able to call the bonds immediately even if they wanted to. Finally, recalling the old bonds and issuing new ones involves non-trivial flotation costs, which can be a significant expense for the issuer. Therefore, all of the above factors may prevent the immediate call of callable bonds after a rate decrease.

Callable Bonds May Not Be Called Immediately After a Rate