I think it is unlikely that the failing septic is cusing your washing machine problems. The only way it could cause problems is if the liquid cannot get out into the soil and is backing up through the tank and prteventing your rinse water from being dumped. If this is the case,then when your washing macine is emptying, your toilets would also back up if you tried to flush them at the same time. You could test this out. Another way to check, would be to get a 40 Litre drum and discharge your washing machine directly into it, instead of into the drain – if your wash comes out clean, then this would indicate the septic blockage is causing the problem. Washing places the largest flowrate into the septic, and is when septic problems are more noticeable. Hope this helps.