Basic Local Alignment Search Tool (BLAST)
Because it has a poor statistical model. It's basically a local alignment tool aided by a fixed-length k-mer index. It estimates homology in terms of sequence identity and while this is often enough to find homology in relatively conservative sequences, the heuristic scoring model doesn't really allow to search motifs. A motif in terms of bioinformatics can be seen as a series of state-switch events, hence you need a model that estimates similarity in terms of likelihood of observing such a sequence of state switches under  your prior state-switch matrix (inferred from a training sample). These models are known as Markov models and people usually utilize Hidden Markov Models to find motifs. There are good popular tools, such as HMMER

EDIT as per OP's comment


  As motifs are locally conserved regions &amp; BLAST also performs local
  alignment then why it should not be able to search for motifs?



A motif is not just a "locally conserved region", it's a specific sequence profile. BLAST doesn't extract any sequence profiles, it wasn't created for that. Given a pair of sequences it simply shows you similar patches. Hence BLAST is simply not the right tool for the task. They made PSI-BLAST for that very sake.  
Moreover, many motifs comprise amino acids or nucleotides that can be quite separated in a primary sequence and only get close in a folded (secondary or tertiary) structure. Here your definition of "locally conserved region" fails as does BLAST.  
As I've already mentioned, BLAST performs a heuristic local alignment, that is it assumes that two related sequences must contain at least one common k-mer (word) of specific length. This, given a precomputed word index, significantly increases performance in terms of speed and RAM consumption. But similar motifs can be present in non-homologous sequences or in highly divergent sequences that hardly evince any homology, and BLAST won't find anything at all.