This problem is quite hard to explain so I will demonstrate with an example.
Say I stake $£1$ on a horse (odds are irrelevant at this point) to win a particular race. The horse loses, so I decide to place a bet on the next race to try and recover my loss. If the next horse has decimal odds of $4$ (or $3/1$), I can work out that my next stake needs to be $(£1 / 4) = £0.25$ to recoup my previous $£1$ loss, but this does not account for the $£0.25$ stake I had to place to win the bet so if the horse wins I actually make a loss of $25$p.
How can I ensure my stake will take itself into consideration when calculating how much I need to break-even?
You have given up £1 already. Suppose you then place a stake $S$, so in total you've handed over $1+S$. If you win with odds of 3/1 then you receive back your original stake $S$ plus $3S$, i.e. $4S$. So you want $4S\geq 1+S$ which rearranges to $S\geq \frac{1}{3}\approx 34$p.