as supplement: this is definitely the problem, use always placeholders! some values have to be quoted so the db knows where the value ends. also you you can speed up the inserts by reuseing your statements and performing them all in one transaction.

$dbh->do('BEGIN TRANSACTION');

my $sta=$dbh->prepare("INSERT INTO ISP(Store,Date) VALUES(?, ?)");
my $stb=$dbh->prepare("INSERT INTO UnityPrimary(Store,Date) VALUES(?, 
+?)"); 
my $stc=$dbh->prepare("INSERT INTO UnitySecondary(Store,Date) VALUES(?
+ , ?)");

while (<CSV>){
  chomp;
  my($store,$isp,$pri,$sec)=split /,/;
  $sta->execute($store,$isp);
  $stb->execute($store,$pri);
  $stc->execute($store,$sec);
}

$dbh->('END TRANSACTION');
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oh yes, and definements like INTEGER or CHAR[9] mean nothing to SQLite2. the only column define which is usefull is PRIMARY KEY INTEGER for self generating unique keys.

update: just for your information, DBD::SQLite $VERSION >= 1 is actualy SQLite 3, DBD::SQLite2 was made to update the SQLite 2 path. just in case you want to benefit from the new features in v3 but didn't know how weird the modules are named.