It's very likely a hardware limitation again - this time on number of hardware lights.
Maya does all of it's hardware rendering ( hw renderer and everything in viewports and editors ) using rendring api called openGL. OpenGL has, by it's design, a limitation on number of lights in can render per frame. And it's 8. It's a bit silly but openGL is rather old and when it was first standardized 8 light limit probably sounded like a good idea.
When OpenGL was introduced not too many cards had a feature called "hardware T&L" ( t and l stands for transform and lighting ). This is a commonplace today and it enbles your card to do all of the vertex transformation and lighting claculations on hardware level at virtually no time cost.
In order to do lighting part of T&L a program need to upload lights data into the card before the frame is rendered. Now, number of lights that card can handle is limited ( to something like 8 or 16, probably more on newer card ) The limit will eventualy die with domination of pixel shader cards - but that's another story.
So if you want your hw rendering to be executed correctly on any hardware, you should respect the OpenGL limit of 8 lights. Even if your gpu supports less than 8 hardware lights OpenGL guarantees you that it will be rendered correctly but in that case needed lights will be calculated by the cpu - meaning a bit of the software rendering calculation - which is slower.
Most of todays gpus handle more than 8 lights and OpenGL can accesss them thru OpenGL extensions - but if you force a large number of light that exceeds hardware limit rachable thru GL extension you can expect all kinds of funky random behaviours - depending on your card, drivers, number of requested vs. possible hw lights, the logic maya hw uses to prioritize the lights etc.
Again, look into specs and try to respect the limits. If you absolutely need a large ammount of lights try to render in multiple passes each using 8 ( or whatever the hw limit of your gpu is ) lights. Then composite the passes using additive function ( screen )
However it may be that this in not the problem in your case. Put the number of lights under control and see if it helps.