As the description of this petition registry documents, the constitution permits the public to petition it's government. The constitution does not put a time limit on the ability to petition therefore it should remove the existing 30 day time limit.
The 30 day limit puts a money requirement on the petition. Those with enough money would be the only group with the ability to promote their cause within 30 days.
Why should it matter how long it takes a group to communicate their petition so long as it is the vote of the people? It does not matter if it takes 30 days or 6 months so long as you get 100,000 signatures.