They recently (Tuesday) changed the way ECM works, so maybe check the notes. I don’t think the new rules are suppose to work the way you are describing but I could be wrong. Really you should just keep the Burner at range (30kish) and jam it instead. When it retreats - and you follow - the Logis will usually keep moving forward and you can attack/kill it when they are out of support range. Its a lot faster. Or switch to the polarized Garmur as shown in this thread: Burner Mission - Ship advice to solo them including fittings
What kind of ship/fit do you use?