Yes. ISP proxies renew indefinitely, and the same IPs carry over each time. Renewal does not change your IPs.
Renewal is automatic
All ISP orders renew automatically by default. You do not opt in, and nothing is needed to keep your IPs.
At the end of each billing period the order renews and your IPs carry over.
Renew, extend and swap are three different things
Only one of these three changes your IPs.
Only Swap IPs gives you different IPs.
Where to manage renewal
Go to ISP proxies -> My proxies, open the order, click Details, and find the Settings section. Extend, Cancel and Swap IPs all live there.
Extend is also a button on the order row in the My proxies table.
Keeping the same IP means keeping the order active
Renewal is indefinite while the order stays active. What is not guaranteed is getting the same IP back once an order has ended.
There is no grace period. To add time manually, extend at least one day before the expiration date.
If an order expires, its IPs go back to the shared pool. A new order gets new IPs, and the earlier ones cannot be reassigned.
Cancelling stops renewal at the end of the period
Cancel turns off automatic renewal. It does not end the order straight away.
The order runs to the end of the current billing period, then the IPs are released.
Terms are locked at purchase
ISP terms are 30 days or 90 days, chosen when you buy. Renewal uses the same term length. 
