At my house in particular, we had same problem, signs of water
infiltration over the years. The previouse owners had almost taken care
of the problem by doing a few common sense things. The first thing they
did was install new gutter system. The second thing they did was
regrade the exterior landscape. The third thing they did was install a
Concrete walkway around the house with a gentle slope away from the
house. These three things almost entirely fixed all the problems.
Unfortunately we had same problem you do, which was once in a while
during a hard rain or watering the lawn near the house, caused a very
small infiltration of water at one side of the basement, always in the
same place. Opon thinking more about this I noted that the grass on
that side of the house was of poor quality, not growing well and in a
very sandy soil. We rototilled the soil to loosen it up and dug it out
for about 18 inches deep. Replaced with a good top soil, grew new lush
grass. This seems to have solved the problem. Zero water for over a
year now. The problem in our case was the grass would not absorb the
water penetration. Then the water would get down into the sandy soil,
follow a tree root to the edge of our basement, where it had a natural
underground "spring" directly to the edge of the foundation. Hope some
of this helps you to at least think of the different things than can
help cause your problems.