If you aren't happy with the progress of a project then first raise your concerns with your Freelancer on your WorkStream. Most Freelancers on PPH cares a lot about delivering a great service to their Buyers not only so that they can get paid and earn great feedback but also because they want to earn follow-on work with their happy Buyers.
The rule of thumb on PeoplePerHour is that you pay for project; if the project that was agreed (either as part of the proposal acceptance processor as defined in the Hourlie description) has not been delivered within the agreed timescales, then you don't need to pay and you are entitled to receive a refund of any money held in the Escrow account for the project.
A few things to bear in mind:
If the Freelancer has delivered the work that was agreed but you aren't happy with the work based on taste (for example, a logo design isn't quite what you had in mind) then the Freelancer is entitled to receive payment for the work as long as they have given you at least two further iterations to try and meet your needs (most Freelancers will go even further to keep you happy).
If the Freelancer is late in delivering the work because they were held up awaiting instructions, materials or input from you then the project cannot necessarily be regarded as late. We always encourage Buyers to provide the Freelancer with everything they need up front as much as possible and be available to answer questions during the project to progress things along. If the timescales look like they are slipping unavoidably due to your own constraints then simply agree revised timescales with your Freelancer so that they know what they need to aim for.
If you have canceled the project due to a change in your needs and the Freelancer has spent time working on the project then the Freelancer is entitled to ask for payment to cover their time; this may include the full deposit sum in Escrow.