I fixed a rate with the service production. Will a live rate override it?

Set that currency to a manual rate in Conversion Currencies, and it holds at your figure until you change it yourself. Every row there is either live or manual, and a manual rate is a number you typed, so the budget prices at the rate you agreed for the length of the job.

Fix the rate

Open the sidebar Info tab. Conversion Currencies sits directly under Budget Currency.
Find the row for the currency. A currency used by a Cost Item is listed automatically. If it is not there, click the + beside the heading and pick it.
A live row carries a pulsing green dot on the left. Click the dot. The current rate is stored and the number turns into a field you can edit.
Type the agreed rate and leave the field. The row now shows a hollow circle, which means manual.

A row you add yourself with + arrives as a manual rate, started from the current live rate and rounded to four decimal places. Overwrite it with your contracted figure.

Good to know

Type the agreed rate as a positive number, then read the field back once to confirm your figure is in.
A manual rate takes as many decimals as the contract states. Only the starting value is rounded to four.
To return to a live rate, click the hollow circle. That replaces your stored number with the daily live rate, so note the agreed figure in your job file first.
A currency used by a Cost Item stays in the list while the budget uses it. A currency you added with + and no line uses can be removed with the - control on its row.
If live data was unavailable when you added a currency, the starting value is 1. Replace it with your agreed figure as part of the same step.
A currency appears once in the list. The + picker offers the currencies that are not already there.
Live rates are a daily snapshot, so a fixed rate is the right choice for a long bid.
A manual rate holds whenever one of its two sides is the Budget Currency. After you change the Budget Currency, check the list and fix the pairs you want held. See The client wants the whole budget in another currency.