So this is just compatibility between this mod and Mekanism. The problem occurs when I connect a "Mechanical Cable"(from Mekanism) or a "Universal Cable" to the power ports or fluid ports. Subsequent reloads of the chunk where they are connected or reloading the server cause the machine and pipe/cable to no longer be connected.

I'm using mekanism with other mods such as Thermal Expansion and Minefactory Reloaded without getting these problems on their machines. I can provide more details if need be.

Which version of BR are you using and which version of Mekanism are you using? I haven't heard of this before; do you know if this started happening only with the BR 0.3.4A update, or has it happened with all 0.3 updates? Was there an update to Mekanism recently which may have broken this, or has it been happening for a long time?

It is Big Reactors ver 0.3.3A and Mekanism ver. 6.0.5.46. I'll try the latest versions of the two in a separate game and see how it goes.

If you've got the time, I'd also appreciate backtracking and seeing if this happened with older versions of Mekanism as well (e.g Mekanism 5.x)

Sure, I'll update you with my results.

So I tested out with Big Reactors ver. 0.3.3A, 0.3.4A2, and 0.2.15A. As far Mekanism only the previous 4 versions were kept that I could find to download. .42, .43, .44, .46. All combinations provided the same result.

Found version 5.6 for Mekanism in a Modpack but it requires the use of 1.5.2.

I think fix b77ee4a for #246 should resolve this issue. It will be in an upcoming release, likely 0.3.5A.