Electrolyzers, unlike other machines, need to be directly adjacent to a power source (MFE or MFSU). They can be against any side of said source, but must share a side with it rather than be connected via wiring.

Easiest solution is to just place your electrolyzer next to your MFE.

Additional info: industrialcraft wiki

To explain why this is, it appears part of the function of the electrolyzer is also to recharge the MFE or MFSU. This gives you a way to store excess power at the cost of some efficiency, but with the benefit of being able to move it later (in the form of the electrolyzed water cells).

Electrolyzers, unlike other machines, need to be directly adjacent to a power source (MFE or MFSU). They can be against any side of said source I believe, but must share a side with it rather than be connected via wiring.

The solution is to just place your electrolyzer next to your MFE, leaving the normal output face of your MFE open to run cabling to your LV transformer and other machines.

Additional info: industrialcraft wiki

To explain why this is, it appears part of the function of the electrolyzer is also to recharge the MFE or MFSU. This gives you a way to store excess power at the cost of some efficiency, but with the benefit of being able to move it later (in the form of the electrolyzed water cells).