If you average purchase price goes up, that means that the price of the fund is going up, which means that the money that you already have invested will grow (and by more than your average price goes up).
For an example, let's say that the fund is at $100 and you have $10,000 invested (100 units) with an average purchase price of 90. Suppose it goes up 5% one month to 105 and you invest another $1,000 (9.5 units).
You now have 109.5 units with an average purchase price of 91.3 (
(90*100 + 9.5*105)/109.5) but your overall investment is now worth $11,500.
Now that the fund is at it's peak
You have no way of knowing this. In a bull market, funds are often at the highest point they've ever been. If you think the fund is now overvalued, then it's fine to diversify into something else. But you may miss out on future gains. So it's a risk either way - that's the nature of the financial market. An old adage is "time in the market beats timing the market". If you are investing for the long term (10+ years), then trying to sell before the dips and buy before the gains is futile since you'll be wrong half the time (statistically) and your bad guesses will even out your good guesses (or possibly worse). Learn to endure the dips (even buying more so you can "buy low") and you'll be fine.
Another option would be to start diversifying into different (orthogonal) funds. If you want to reduce risk, invest in a fixed-income fund. Or add an international fund, or a small-cap fund if your fund is a large-cap (e.g. S&P 500).