In the more difficult moments think less about the run you're doing and think more about the goal further down the line if you have one set. As already mentioned. it replaces any doubts that might enter the mind concerning what you're doing this for when you could be at home doing something or nothing else instead. Interruptions to your running journey of reaching your goal occur at anytime, before, during or even occasionally after a session. Also just be wary that lacking motivation may be as a result of setting your aims unrealistically high, so therefore overall there's everything to gain from lowering them, just as long as you're mostly feeling that the running journey you're gradually creating for yourself continues to feel worthwhile to you or for those you're intending it to benefit.
Good advice from mathschick. Also do run in the week but if you can try to mix it up to keep enjoyable - 10k every other day sounds like too big (and I'm also thinking unneccessary) a challenge right now, but you have already found that out yourself.
It is a bit confusing because I always thought you recover from injury and rest during days off. But now I gather runners tend to only rest when they are suffering with an injury, and recover when easing up a bit after consecutive weeks of hard training. Perhaps rest days or longer periods of not running don't come into it when you are fit? But experts advice I've read is to always respect days asigned for rest, while recovery weeks (running on average less than you're used to) will ideally finish with a race of a shorter distance than you're training for.