Intriguing, I only ever had this issue when ping was above 500 (due to other people downloading etc.)
Were you perhaps having an extended lag spike during the time you tried to heal?
I can say from experience that having a low FPS can indeed cause this problem. When I was using a weaker graphics card, this happened frequently. If I remember correctly, setting the max FPS to around 35 prevented this somewhat.
It seems odd that limiting an already low FPS can help in any way. I can only speculate that by removing spikes, it keeps the FPS more stable allowing for more reliable medic box/barricade deployment.