The most important single thing to check - the cause of almost all multicast problems, in fact - is that your router is actually configured to generate IGMP queries. What you describe are typical symptoms for not having an IGMP querier.
If IGMP snooping is enabled in the switches, they see the initial IGMP group subscription sent by the hosts and assigns the switch port to receive traffic from that group. However, that membership will rapidly time out unless it is refreshed, and the IGMP protocol spec requires that a router issue IGMP queries which get hosts to re-subscribe. This process of the router issuing queries and the hosts re-subscribing is what keeps the group memberships live in the switch. If this is not configured, multicasting appears to "work" briefly but then stops.
IGMP querying is independent of PIM, which is a router-router protocol for creating wide-scale groups. You also mention "Cisco multicast" which is presumably CGMP, but CGMP is a router-switch protocol and it does not function as a substitute for IGMP.
The easiest way to verify that at least once device is configured as an IGMP querier is to perform a packet trace using a tool like WireShark. You should expect to see IGMP query messages from the router to 224.0.0.1 (the all-hosts group) fairly regularly, at a frequency high enough for the switches to not time out the host group memberships. A typical querier will transmit every minute, while a typical switch timeout is 3 minutes.
Beyond that, the only thing of consequence related to VLANs and multicast is that many switches have a limit on the number of supported simultaneous multicast groups; when partitioning the switch ports into VLANs, for many if not most switches that internal table ends up being divided amongst the VLANs (so, a switch that supported 32 multicast groups would only support 8 groups per VLAN if there were 4 VLANs). Configuring large numbers of VLANs can thus end up meaning no individual VLAN can support enough groups to actually function using multicast IP.
I don't think that concern is likely to be related to your situation, but if your switches do have a group limit like this, it would be a good idea to find out what it is.