Not really, no. It's actually a grammar mistake. Instead of using the word "that," it would be more correct to say "during which," or "when":
"There was a period of time [when/during which] new entries were not being saved."
Using "that" instead of "when" is a fairly common mistake among native speakers, because we can use "that" in other structures that sound similar: "There was a dog THAT ran away." "There are papers THAT I need to write." The word "that" doesn't imply a time relationship, so it shouldn't be used in place of "when," but it often is. For instance, people often say things like "there was a time that I was dating him" instead of "there was a time WHEN I was dating him."