Well, I did it for a number of days with eyes open trying to fix the eyes at 1-2 meters, at a long distance, concentrating on breath, on the visual objects, on body sensations - all with a similar result. The problem here is that tension around the eyes arises and persists for long periods of time during meditation, which, when practiced over the course of many days, accumulates and does not completely disappear even after a good night's sleep. Some tension may be a natural reaction, for example, when an eye is suddenly exposed to a bright light. However if ignored, it disappears quickly, so it does not bother me. I noticed several sources/types of persistent tension during meditation:
1) Firstly, when I just started doing concentration meditations, my eyes(when closed) would try to focus on whatever spot the mind was focusing on. The method of keeping the eyes open seems to target precisely this problem as the person has some idea of what the eyes are doing and can correct them if needed. With exprerience this tendency seems to be disappearing.
2)Secondly, continuous conscious effort to pin the mind to the object of concentration produces a byproduct of tension. The more the mind is caught up in something, the more effort is needed to return it back to the object quickly. Unfortunately, this also means that more tension will be produced as a result. It is as if part of the fuel intended for concentration was diverted to unproductive activities. Only when really tiny amount of effort is applied no noticeable tension tends to arise, and when it does arise, it quickly dissipates. Anything greater in the long run leads to the problems described above. On the flip side, with such a small degree of effort the mind is not very inclined to stay concentrated.
3)Finally, when tension arises for one reason or another, it may spiral out of control, if there is an aversion to it. It would go something like this: Initial tension-->aversion-->more tension--> more aversion, and so on. It seems to be dealt with by observing it with equanimity.
Thus it looks like my question is mostly about the right effort.
A lot of effort -> quick and stable concentration; a lot of tension.
A little effort -> not so quick, but eventually stable concentration; some tension accumulating over time.
Very very little effort -> little to no concentration(even after 1.5-2 hours); no tension.
I am not sure which approach(amount of effort) is more useful in the long run, as each one has shortcomings which I have not been able to overcome.
This is all in reference to concentration meditation. Generally, I do not experience this issue with mindfulness meditation, as the goals are slightly different.