After about 18-24 months they raise the next fund.
With the GP I work with there's almost no overhead, just two GPs and the annual accounting. The annual accounting and tax filings can cause additional capital calls (small amounts, US$1500-2000).
As an LP (and a tiny one at that), one of the problems I'm seeing is that companies are raising ever larger up rounds at ever increasing valuations, giving away massive preferences to the later investors. This boxes the companies into seeking either grandiose exits justifying the valuations, or they wipe out the early investors (and employees) because of the preferences overhang with the finial investors (typically institutional money).
It's been an eye opening experience, I've learned a lot. Unsure how much more money I'll commit to investing this way though.
The funds I'm in don't take board seats, though they do offer access to its network of investors and contacts to the companies it invests in. Different funds are run different ways. The GPs of the funds I'm in do not do this as their primary job, other funds have principals (GPs or other forms of partners) who draw their income from the funds in one way or another.
Other considerations: the funds have a limited lifespan (I believe each of the three I'm in are 10 year limited partnerships with an option to extend by simple majority vote of LPs). Because they're limited partnerships, the returns get reported as income to the IRS, and I'd owe taxes on them, even if they were not distributed, which is another reason not to re-invest returns (if the returns were re–invested, you could potentially pay taxes on income which then gets "lost" when re–invested in a startup which fails).
I commented elsewhere in this thread that so far across three funds we're seeing the 33% fail, 33% break even (modest returns) and 33% either have returned the fund or have potential to do so, which is a pattern I've seen repeated by many venture funds over the years I've been following or investing in them.