Here is some exciting textbook reference (Janeway 5th ed.):
See Figure 8.14 and compare with text. Whereas the figure shows some presentation of antigen at the site of infection, the text does not explicitly refer to the figure of the site of infection, and says that presentation of antigen happens only after (maybe during) movement of that same APCs from the site of infection to the lymph nodes. It seems to be only there that presentation takes place (and, presentation by dendritic cells means priming, defined by environment of lymph node, in contrast to presentation by infected non immune cells).
My point is that presentation does NOT happen at peripherical sites of infection which is contrary to the statement in your question. According to Janeway's wording - taken literally - before priming in lymph nodes has taken place there is no danger to dendritic cells in presenting at the site of infection. Successful presentation in lymph nodes thus becomes a prerequisite for any killing of presenting APCs. This looks like some self-regulatory mechanism to me.
It's a different question if, while protecting during the priming process, the "known" (your question is based on the premise that there is no killing during priming) second signal B7 in presentation induces tolerance for a certain time period. Again, according to basic textbook wisdom, at lymph nodes "presentation is priming". Presentation at site of infection by APC is no priming. Priming means that t-cells are given permission to divide. It is not trivial to see: APCs, dendritic cells, must be protected in lymph nodes "only", as it is "at that point" they are doing their job of priming. When they present the antigens in the lymph nodes they meed naive T-cells that have yet to become cytotoxic - which implies a time lag for cell division and expansion of the t-cell clone. Before naive t-cells have divided and differentiated there can be no killing. The effet of B7-receptor might last that long - within that time lag a few other specific t-cells might presumably have been primed, then the APC might simply not be needed any more.
Question of S. Oncosuresh at researchgate at https://www.researchgate.net/post/Why-Dendritic-cell-are-not-killed-by-T-cells-when-they-present-antigen
It is the "speculative" answer by Ye Tian from the University of Chicago which I feel inclined most to: cp. "... if by then" (they will kill the DC's presenting).
You say, quote: "... and travels to the tissue, where it again finds APCs presenting the offending antigen."
It's a possibility that the assumption that there is presentation by dendritic APCs at site of infection is wrong.
In that case the following reasoning applies: If there is presentation at site of infection presenting dendritic cells in fact are being "simply" killed as they are not needed any more, as the very fact that they meet primed(!) cytotoxic t-cells shows that presentation in lymph nodes for purpose of priming has succesfully been undertaken "already".