I don't know the answer to this and am responding purely out of interest and idea sharing, since I like the question.
Could this work as a Parametric intensive computational statistical approach;
1) Define a universe of positions the portfolio can feasibly hold, and model each with some assumption about default over a given time period (statically at first for simplicity).
2) Initially create your portfolio with a random allocation of a subset of feasible positions (all same notional for simplicity).
3) Randomly simulate some defaults within your feasible space and record those held in your portfolio.
4) Parametrise the 'churn' of your portfolio since this characterises its fluctuation; after each period choose $N$ closed positions and $M$ new positions where $N$, $M$ are your parametrised random variables and then randomly select those numbers of closed and new positions from the relevant sets. (choose from distributions that average a constant size portfolio)
5) Repeat 3) and continue until enough periods have been measured to return a default rate over the complete period.
6) Perform enough experiments to take an expectation of the long term default rate.
Under this procedure, if the rate of default on every position was the same, I expect that mathematically the churn parameter will do nothing to the expectation of the long term default rate. It will however increase the variance of the estimator since for each trail the number of holdings can increase significantly or reduce significantly and this will impact the final result.
I recognise a strong critcism of this model is that it is parametric and will likely miscapture some facets, and of course requires calibration. The problem with your approach, although, non-parametric is that it assumes the position is held for a period of time that it may indeed not be. I'll have a think about how one might go about a non-parametric bootstrap procedure, to account for this.