えぐみ　＝a bitter taste; a tang　
この竹の子の煮付けはちょっとえぐみが残っている。
(Source: Shogakukan Dictionary)

In your sentence the English can be translated as:
...えぐみが強くなり= the bitterness became stronger

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Note added at 16 hrs (2010-09-27 04:29:24 GMT)
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Here is the translation from the dictionary about the 竹の子 example I gave you:
この竹の子の煮付けはちょっとえぐみが残っている
= This boiled bamboo shoot is still a little bitter.