The fact that you have at least received a payment is a good sign that your masternode is working on your end. Right now there are some major issues being worked out between masternodes and miners. The team is working on some very big decisions for the future of Chaincoin. Once a decision is made an update will be released which should improve Masternode Payments.

No, there is no need to keep your wallet open on your desktop as for the functioning of the MN.