There are a couple of reasons why this may be. Firstly, check that you’re drinking as advised in the bottle’s user manual. Some filtered water bottles are designed for holding below your mouth and sucking up through the straw, rather than tilting your head back and trying to drink with the bottle angled upside down.
You may also find that water passes up through your straw at a much slower rate if the filter is damaged or clogged. If you’ve had your filter for more than a month, or used it frequently, it’s most likely a sign that you’re in need of a new one. The longer you use a filter for, the slower it will become in filtering your water.