Ok, Gulo.
We wont call it fear -- lets call it 'a lack of comfort'.
I, like many MArtists; was a 'range' fighter in much of my training.
At work - before Systema - I discovered that being 'uncomfortably close' was a 'range' that I could move effectively in...but my attackers could not. They needed the distance to launch what they believed were powerful strikes. My closeness made it easier to 'shut them down' before they could launch powefully.
In Systema, this ability I was developing on my own was a part of 'the work' and I took to it well.
You will also. It is not so much fear -- just something that time will bring to you through experience, as it probably is already.
If I might make a recommendation - I sometimes do this with a student who feels uncomfortable 'attaching' - - do some movement drills and unbalacing work with your eyes closed of blindfolded. This way, your sensitivity is relied upon heavily and you will succeed only if you remain close and attached to your partners bady movements.
Give it a try - it will probably help abit.